First of all, I already changed it so that supply points as they existed in 1E/2E are replaced by supply depots. Your homeworld* is going to act as a limited supply depot, resupplying units in the same system, just to cover situations where an empire lacks the tech of finances to afford one.
*I am using this term instead of Capital, because I really don't see any point in keeping the Capitals around at this point. They really don't serve any significant purpose. We can just say that Homeworlds have the limited supply advantage and be fine.
The reason for this change is that is exposes the supply infrastructure to enemy attacks and makes the game generally more interesting. Before you couldn't disrupt an enemy's supply network because the colony WAS the supply network. Now, you could conceivably launch a lightning raid deep into enemy space to generate a Defensive scenario and knock out their supply depot.
The rules for supply routes also need to be made clearer. The 2 jump rule is fair, but then you start getting into the "except if it's Tuesday, and Mars is in Aquarius, then you have a royal Fizbin" situations. Let's break some of those out.
Restricted Lanes
This is probably the big one. VBAM up to this point has said that you can't trace supply over a restricted lane, then provided some finicky rules for using Supply ships to bridge the gap. I do like that the restricted lanes are too hazardous for civilian traffic and that it blocks supplies, but trying to mate up Supply value to jump across the lane is kind of tedious.
Instead, while I was doing some other things around the house today, I had this thought: what if a fleet could still trace a supply route over a restricted lane as long as there was a Supply ship in his fleet? This would represent that the Supply ship was helping to keep the fleet in supply by making trips back and forth to meet up with military-grade supply ships. It is gamey as all hell, but it's an easy check to verify that a fleet or system is in supply.
Speaking of systems, if having the Supply ship in the system might be enough to keep the supply route active and keep the entire system in supply.
You could extrapolate the above and say that the system can remain in supply as long as there is an amount of Supply based on the distance from the supply depot. This would be 1x for 1 jump and 2x for 2 jumps.

Referring to the above example, let's assume that the Blue player has a supply depot in the Home system in the center of the map and he wants to get supply out to Minanao. Right now he would have to put Supply ships in Formosa and another in Mindanao and match them up, and the number of squadrons resupplied is based on the Supply value.. yadda yadda yadda. Instead, we could say that just having, say 4 Supply in Mindanao would be enough to trace that supply route and keep the system in supply from Home. That would be 2 Supply per jump as the requirement. For a lower tech empire, that is going to be 1-2 Supply ships that will have to stay there and not get crippled.
Contested Systems
Another sore point that we have is what happens when there are enemy fleets flying around causing problems for your supply lines.

My current preference is that supply routes can traced INTO but not THROUGH contested systems. For example, the Yellow supply depot in Truk could trace supply to Soela (contested), but it could not trade supply beyond that into Rennell or Wewak.
The Green supply depot in Soela is more of a special case, and one worth examining. If this is the situation in the Supply Phase, would Green still be able to use that depot to get supply out to the other colonies? I'd say it could resupply friendly units in that system, but the enemy presence is going to make the regular dispatch of supplies out of the system dangerous. This isn't strictly a blockade situation, but I think it would disrupt the supply depot.
Thinking about it some more, we could use a system similar to what I described for Supply ships extending supply over restricted lanes in this context, just with the Blockade Runner ability. So if Soela is effectively blockaded for the purposes of supply (and ignoring that Rennell already has a supply depot!), maybe having 2 Blockade Runners in Rennell would be sufficient to keep the blockaded supply lines open? That would give Blockade Runners an actual strategic ability, and one that would be useful during wartime.
Of course, we wouldn't want systems to be blockaded by a single ship, but if the number of enemy ships is greater than or equal to your own number of ships, then I'd say that the system would be "blockaded" at least for the purposes of supply.
...
Wait a minute. What if Supply ships worked exactly as I described for restricted lanes, but that applied to ALL military adventures beyond supply lines? For example, if I am 3 jumps from a friendly supply depot I would then need 6 Supply to remain in supply? The Supply ships would then not be consuming supplies so much as extending the effective range of your supply route. That would turn Supply into a passive ability that you wouldn't have to track and reduce upon use.
Combined with my original thought, it could even be as simple as "Fleets that are out of supply can use Supply ships to establish a temporary supply route back to a friendly supply depot. The maximum length of this basic supply route is equal to the total Supply functions in the system." So you'd get the 2 jump basic supply route everyone can use, but beyond that you're going to need Supply ships, and enough Supply to get a meaningful extension. This would make exploration a bit easier on players because sending 2 x Supply 2 ships would let the exploration fleet travel out 4 jumps away from base and still be in supply.
Planning for deep range military operations also becomes easier because you can just make sure to add enough Supply ships to your fleet to be able to maintain supply at that distance. But in so doing you are leaving yourself open for the enemy to target your support train via includes and cripple or destroy them. You'd then find yourself stranded and out of supply and racing home before you took too many losses.
That to me sounds pretty COOL. It solves the problem of long range deployments while also eliminating the goofy supply ships across restricted lanes problem.
I also like that Blockade Runners would have something to do, and the ratio of Blockade Runners needed to maintain supply could be related to the force imbalance at the blockaded supply depot. For example, if Yellow had 10 units and Green only had 4, then you'd need 6 Blockade Runners in any system within 2 jumps that wants to keep that basic supply route alive. Since it's all based on number of ships, most Blockade Runners are going to be Corvettes or Destroyers: cheap to build, probably Atmospheric so that they could be built in the back country.
Blockades
I guess it's worth throwing this topic in here, too. Do we want to make blockades as simple as "there are two hostile forces in the same inhabited system, and the defender has fewer ships than the attacker"? And other than supply, what other consequences should there be? Should the local economy completely go into stasis with no income or unit production? I really am not sure what the right answer is here. In a larger game having a world be blockaded doesn't hurt, but if it's your homeworld and you lose all of your income then it's pretty much game over.