wow, so many posts, so much to read.
in any case:
1) the weapons 2 upgrade of some bases do not actually increase range, but add another weapon type with longer range. the old ones stay the same short.
2) the actual range upgrade (for all types) sounds like a workable solution, but nevertheless the basic range has to go up. quite a bit.
3) the PJI idea (the old one of beta that totally blocked phase travel) also sounds like a good idea, but also very powerful and more of a hard solution, when a softer one is usually better, you should be able to go around it, but only at a price/ at some effort.
4) starbases ARE not only military ojects. I upgraded the vasari ones with both pop upgrades and the trade module and it gave me about 2,5 + 1.1 = 3,6 or so creds. which is quite substantial imo. and the CAN fill the gap of trade lines. in my vasari game I established a long trade route which was connected through a dead roid via a starbase (and ended in one). tec ones are also useful with their repaid and construction upgrades, avents seem to have culture spreads. so there is definately a non-military use to them, if you want it. and that's what I think is great.
5) about stars and gas giants. I set up a vasari starbase in a star grav well and was suprised. the star is so big, that the actual grav well is only a fairly narrow band which is in its breadth pretty much completely coverable with a vasari starbase. so ... if you put it in the beginning or end, it should reach most ships.
and for gas giants .. well, haven't had any so far in entrenchment, but it might be interesting if the planets were enlarged vis à vis the total grav well. that way you could have a large total area, but it would be more of a travelable ring whose entry points can be guarded via a starbase. it does become a problem with multiple lines though I'd say.
6) starbaes in enemy wells. large penalties in setup and upgrade times, plus a general increase in their set up time should fix it. if it takes 5 mins to construct one in an enemy well, I don't really see much problem. after all, leaving him alone there for so long, you deserve punishment. and, as has been said, vanilla starbases aren't that much of a threat. if the upgrades are also increased, I'd say it's cool. viable as an offensive tool, but you have to prepare it and bring a fleet to defend it until it is ready to fight for itself. but it should definately stay as an option.