As a caveat, most of this post was written yesterday before I ran out of time to get everything together for posting. As it is it's past midnight here and I'm starting to get a little rummy, so if things seem disjointed or don't make sense, well, join the club!

Research
Tech and research has been a major concern for me going into the final stretch of development. Some permutations of the tech rules have worked but allowed research to proceed too quickly. Others mitigated the effect of research and left players actively scrapping their Research infrastructure because it just wasn't going to be useful for them during the game. Finding a useful middle ground between these two extremes has taken time, but based on my current test game I think I have managed to find one.
As currently written, your tech advancement cost is equal to 50 times your total Census. The size of your imperial population is used here instead of your total income because it's too easy for a low income empire to tech if they have another power available to feed them economic points. This is still a problem using Census, too, but it's not pronounced and can be addressed by having minimum tech advancement costs.
Your colonies produce a minimum amount of tech investment each turn equal to their utilized Research values. An empire may purchase additional tech points at a colony, up to a maximum equal to 5 x Utilized Research. This sets up a situation in which Research infrastructure is still useful (free tech points) but that you may not need to build everywhere if you don't want to. Maximum tech growth will encourage you to max it out, in he same way that you'd max out Economy to earn as many economic points as you can. However, colonies with Research infrastructure can be captured by enemy forces and provide them with research data to boost their own research efforts. That means building large research bases on a hostile border is probably not going to be the best idea.
Using this research system it took my player empire about 20 turns to increase its tech level by 1. I wasn't putting much into tech each turn, and if I'd increased my tech investment rate I could have easily reached TL 1 in about 15 turns. This rate of advance is slow, but it plays well with the ship construction rates. Specifically, it means that I should be able to get a new unit prototyped and built before the next tech level increase comes along. This was a problem when my empire was teching every 10 turns.
Industry
Industry has been changed a bit in that a colony's industrial capacity is now 5 x Utilized Industry instead of Census x Utilized Industry. I discovered that I really didn't like how Industry was scaling, especially the fact that small colonies couldn't build anything. I don't mind having limited building options, but they needed some ability to build something. Now a 3 Census colony with 3 Industry would have an industrial capacity of 15. That's just enough to build a very small battlecruiser (if the system has a Shipyard), or at least perform some smaller construction jobs. Industrial capacity also just limits the total cost of military unit purchases (build or repair) that can be made at the colony each turn. The 1E extended construction rules that have been ported forward to 2E in various flavors typically put the total construction cost of units that could be simultaneously under construction in a system at a level equal to its construction capacity (more or less what industrial capacity is in 2E), but that ends up artificially slowing construction which becomes a problem when larger capital ships can take 10 turns to build.
Right now in my test campaign, my homeworld is working on a number of starship projects and my only limit is that I can only build 30 EP of units per turn. Because units in 2E cost about twice what they did in 1E, those limits mean that I can more or less build 2 heavy cruisers per turn, each of which will take about 6 turns to build. This encourages players to keep military units under construction at their planets, spending points here or there to fill out their forces in expectation of their needs later during the game.
Military Units & Unit Construction
Speaking of military units and jumping to another tangent, one change I have made to military units (and it's a minor one, but with major ramifications) is to change the Command Cost formula so that it's Build Cost (renamed construction cost - more on that later) divided by 5, round down, minimum CC 1/2. This fixes some of the issues I've run into with breakpoints in the unit construction rules. This is combined with a change to Command Rating that currently puts it at 2 x Command Cost + 2. This gives us a command factor breakdown as follows:
Escort: CR 3, CC 1/2
Light Cruiser: CR 4, CC 1
Heavy Cruiser: CR 6, CC 2
Battlecruiser: CR 8, CC 3
Battleship: CR 10, CC 4
Dreadnought: CR 12, CC 5
Superdreadnought: CR 14, CC 6
This makes wolf packs and swarm fleets more effective, and an empire with a dozen small frigates defending a single system can now better concentrate their firepower and have a better chance at surviving against larger ships. It also allows for larger fleets relative to what I was experiencing previous to this rule change. So far so good.
On economic factors, units now have Build Cost (BC), Maintenance Cost (MC), Build Time (BT), and Tech Level (TL). BC is the old construction cost, renamed to not clash with Command Cost's abbreviation, and is the economic point cost to build a unit of that type. MC is the cost to maintain a unit for an entire year, and you pay 10% of it per turn. I think it was Jimmy that was lamenting about the smaller size of the fleets in the previous build of the rules, and to address this I have adjusted MC so that it is equal to Mass divided by 5, round to nearest, minimum MC 1/2. BT is half of BC (round up), which creates interesting decisions given the new CR/CC dynamic where players can decide between wanting a bit more space or reducing their build times. TL is the tech level of the ship and determines where it can be built.
The number of mass units (MU) that a player has to spend on unit abilities is now equal to BC x 2, +10% per TL above TL 0. This seems to give a good range of values given that MU are being spent on three primary statistics (DV, AS, PD) plus special abilities.
FTL, the most common special ability, has been costed at 50% x BC (round down, minimum 1/2). This is high, but given the strategic benefits of faster ships and the rate at which extra MU becomes available at higher tech levels it is currently looking like it should work out (knock on wood). It also creates another interesting decision point when building ships: odd build costs give you cheaper FTL but higher build times due to how the numbers round.
I've also more or less committed myself to reducing the cost of Carrier, Assault, and Cargo to 1 MU, but with the stipulation that each one of these basing abilities can only carry 1 BC of units per point of value. That means that a Carrier 10 unit can carry 10 BC of flights. That might be 10 x 1 BC flights, 5 x 2 BC flights, or any other reasonable combination whose total BC is 10 or less. I've also decided to remove most of the vague launch/land rules I was working on to keep things simpler for the player. The main penalty for carriers will be the expense of maintaining all of their flights, the difficulty building and delivering replacement fighters, and the fact that flights that lose their carriers are abandoned at the end of a combat round. The last point I'm still fuzzy on and need to do some more testing.
Another special ability that I've been fuzzy on is Supply/Endurance. After going back and forth on those I've started looking at just combining them into a single Supply ability for the moment, with each point of Supply (1 MU cost) providing supplies for 1 CC of units when they're out of supply. The Endurance ability itself could then be resurrected as a cheaper version of Supply that only benefits the equipped ship and can't be shared with the rest of its accompanying units. In my current campaign this has worked well for extending the range of my 1 CC light scout cruisers. Each of them has 2 Supply and can be out of supply for 2 turns before they start taking damage.
Emerging Empires - the Iron Sky Law of Imperial Discovery
Jumping to an entirely different topic, I got a chance to put some more time into working on the "Iron Sky" new empire rule which I am currently calling "Emerging Empires". The idea is that in exploration campaigns you need a mechanism to encourage players to continue exploring so that they don't just explore a system, build it up, and then move on in a systematic fashion so as to avoid making contact with other empires. To this end I found the following solution that so far seems to work. Every turn during the Exploration Phase (which will be before Movement) you add 1% to your emerging empire chance but then subtract 1% for every jump lane explored that turn. You then roll D100% against your emerging empire chance to see if a new empire has entered play. The new empire will usually control 5 or fewer systems, but there's a wild card option that would allow it to be a bit bigger. The tech level and number of colonies that it controls are randomized but for the most part the empire will tend to be pretty close in tech to the most advanced player empire.
Based on the Iron Sky rule, I'm also looking at vastly simplifying the existing exploration empire discovery rules so that the only empires that you'll find by stumbling into a system are one system powers that will range from Pre-Industrial to barely Interstellar (TL 0). I might give a bit more variance to allow for a slightly more advanced Interstellar that just never developed FTL drive, but I have to give that some more thought and see how the charts that I have change based on the shift in focus.
Facilities
I've increased the cost of facilities to 100 EP + 10 EP per jump from the nearest capital and restored a 2 EP per turn maintenance cost for them. This makes them expensive to build and maintain, which in turn will encourage players to only build the facilities that they actually need and not just spam them all over just because they can.
Comments on the "Lost in a Sea of Stars II" Playtest
I want to make a few comments directly about the current campaign itself, and in doing so I may end up reiterating points I raised previously in this post, but it's late and I'm ready to type some rambling thoughts before I stumble ignominiously off to bed. This game started out a fairly simple, straightforward test but by the end of Sunday night it had actually found its rhythm and was becoming more than an exercise in rule testing - I was actually having fun playing it. The rule changes that I had implemented going into this game all seemed to be clicking and I had finally found a turn order format that wasn't bogging me down in details.
Probably the best changes thus far has been a gross simplification of the system loyalty and piracy checks in this game compared to previous 2E drafts. I went back to the drawing board to a degree to try and find an option that makes them provide the intended results without anywhere near as much hassle. For system loyalty checks this has boiled down to making a D10 roll for each inhabited system. On a '1' the system loses 1 Morale, on a '10' it gains 1 Morale. The morale loss window increases to '2' for Unrest and '3' for Rebellion but otherwise remains the same. Rolling for my three systems each turn takes a few seconds and there aren't any obnoxious modifiers to calculate.
Piracy checks have reverted back to a 1E style to a certain degree with a percentage chance of piracy, but I may still convert to a D10 if I think I can do it without losing granularity. The piracy chance calculation in this campaign is at a base 5% + 5% per trade route in the system. The negative modifiers are -1% per starship or flight in the system and -1% per Police value. My Sentry frigates have 1 Police value, so each Sentry gives a system -2% piracy chance. That means that it doesn't take many ships to safely police a system. It also gives a purpose for small police ships and warrant cutters, as they are more efficient in combating pirates.
Exploration is so well tested at this point that it hasn't been a problem at all. I have found a few 'bugs' in the system generation rules, namely that star systems seem to have too many jump lanes connecting to them and System Terrain results were too common. I have been tweaking those as I go and think I have the problems fixed.
One other thing that I tested here was giving my player empire 10 times their starting income in military units at the start of the game. That gave the Nova Solar Federation 300 EP of units at the start of the game. While this has been really helpful for me during the early stages of the game, I came to the conclusion while generating the Filosi Consortium that 5 times income is still a much more balanced force size. The Federation Navy is just so expansive that I really haven't had to build any new ships, when I really should have been forced to make a decision to do so at some point before getting TL 1.
Trade is something that I've reworked extensively since my previous draft, and I'm incorporating notes from different players to try and figure out the best way to approach it. In this campaign I am handling trade by having an empire have to add systems to their trade network by establishing trade routes there. The cost to establish a trade route is equal to 10 EP times the distance to the system from the nearest capital or Trading Post. Referring to the campaign map, this means that a trade route between Nova and Pacifica would cost 20 EP to setup. A player then earns 10% of the system's trade value each turn, and trade value is equal to Census x Highest Utilized Infrastructure. Nova has 7 Census and 7 Economy, so it's trade value is 49. The Federation's trade route to that system therefore earns it about 49 EP per campaign year (10 turns). Phoenix meanwhile has a trade value of 9. It cost 10 EP to build a trade route to Phoenix, and with a trade value of 9 it will take a little over a year to earn enough from trade to cover that expense. Pacifica meanwhile has a trade value of 1 and it would take 200 turns to recoup the cost of extending a trade route to the system (i.e., you just wouldn't do it).
I'm liking the feel of this change to trade, though I think the trade route cost might need to be dropped. Oh, yes, I forgot - you only pay 5 EP to build a trade route through a system you are already trading in and the Nova/Pacifica trade route would only cost 15 EP.
I think that's it for the night.