Although, we could certainly address the starbase mechanic by having starbases essentially be mini-planets (blatant stealing from Sins here, actually) in the sense of having influence as well as population, though not necessarily tiles.
starbases essentially be mini-planets
Point noted, and, as you see, I've already addressed that.
You'll also notice that I'm specifically stating it probably won't have any tiles. Also, I'm assuming it will use the planetary pop growth mechanism as well, so dropping a full planet of 8 or 10B isn't really an issue-or at least no more so than it is now.
Bear with me as I delve into an explanation of how Sins handled these various issues and how GC3 might do so as well. (Alternatively, skip to the last paragraph.)
The economic aspect is a bit harder to address in Sins, as most of your cash income is from trade ports (your homeworld notwithstanding), however it is generally accepted that a starbase upgraded with trade upgrades is not going to be a better investment than trade ports around that planet-which is of course a good thing in general, were the delta not so large. Since income in GC2 is based off of tax and tourism, which are themselves both based on population, if we solve population, we've solved the income problem.
The population gap isn't-the Vasari are the only ones with a population module, with two levels of 50 each for a total of 100-which actually may even be too much on a relative basis. A Terran planet has a maximum of 280 population before any research upgrades; Desert and Ice are 190 and 160 respectively. Really the only thing a starbase could beat in this sense is a Volcanic or an Asteroid (70/20)-also as it should be. I'm definitely thinking a small amount of pop for the starbase, but then again I'm thinking of giving initial colonies as well as civilization capitals new population values as well (both starting and final), so I'm not sure what exactly would be a good recommendation at present. (I tried in the final paragraph, though.)
The influence aspect is solved relatively easily in Sins simply due to how slow the influence ("culture") propagates, and even at maximum propagation rate how slowly things change on affected planets-whereas GC2's method is somewhat by necessity instantaneous. So this is the only part where we might have a problem, due to needing the starbase to have sufficient influence to not flip to two enemy planets, but not having enough that it can flip two enemy planets by itself.
So with an initial colony of 8B (TA) and a civ capital of 16B, we might have a starbase of 1B (500m seems too low to do much good, really) and perhaps an influence bonus such that it were considered to be a planet of 5 or 10B for planet-flipping purposes. I'm not sold on the population, though-you'd want it to be at least enough to balance out maintenance, or at least the majority thereof. Obviously this becomes more of an issue with influence starbases, but as you need them in very close proximity to a planet to do much good, it shouldn't change things substantially. (Assuming they get a redesign as well, which might not be a bad thing, this would need to be addressed.) Lastly, one other good reason for starbases to have a relatively low population limit is the need for morale at higher population levels (which I'm hoping gets a bit of a redesign as well), particularly if it's in the absence of tiles to build on.