The absolute pivot would be to strip the Vasudans of their space-Navy. After that, they'd be at the mercy of the GTA (assuming that GTI would not face a Terran civil war at the same time), and no longer able to fight back efficiently.
#1 Has the PVE retained a second strike capability?
Thats an interesting point. However, even though I think that Vasudan resistence would last for quite a while,
one should keep in mind that "resistence in space" follows entirely different rules than, say, fighting for the liberty of your occupied country on 20th century Earth. It requires high-tech if you want to keep up any kind of credible threat, which you cant find around every corner and could easily be brought under control of a Terran occupation - like, you'd literally have to build nuclear weapons in your garage to fight this kind of war. So in the end, any resistence group would run out of ships and ammunition and ultimately rather fight whatever Vasudan puppet government has been set up instead of the Terrans themselves. 32 years after (FS2 time), there'd be likely no resistance left.
#2 "Holding on to a prize as vast as [the Parliamentary Vasudan Empire] isn't going to be easy. It's going to require an enormous number of ships, a massive occupation army, and constant vigilance."
Perhaps GTA would occupy the the Vasudan planetary capitals to install puppet regimes, but in the long run there'd be probably little difference between collaborateurs and "independent" governments if the Terrans controlled the access to space/subspace and hence all interstellar comm/transportation/trade. The only thing Terrans would have to occupy would be the key sectors of the economy - ship construction, and maybe the fusion powerplants to turn them into a pre-industrial civilisation again just by flipping the powerswitch. Occupying habitats possibly doesn't even matter if you can sit in your spaceship and threaten to nuke the planet into a radioactive wasteland.
As the Terran colonies were still poorer than the Vasudan ones, occupying them would be both possible (manpower becoming available due to unemployment as Earth being cut off would still cause a rupture) and immensely profitable (industrializing Terran colonies by ripping off the Zods). Seizing Vasudan resources would help a GTI-run GTA to become popular with the public, and help the central government to gain addontional influence over the GTA-systems and blocks by distritbuting them as they see fit. Furthermore, GTI would have accomplished in a few months what GTA couldnt in 14 years - eliminate the Zods as a strategic threat.
#3a An occupied PVE might become a breeding ground for radicals
As above, whether the Terrans sit in orbit, occupy keypositions, implement a puppet government or capture the entire local government (colony) may not even matter in the end due to the global balance of power. As such, dealing with radicals would be the problem of the local (likey Vasudan) government.
The point is that without high-yield weaponary and subspace drives you are simply unable to fight effectively except maybe occasioal terrorism. Knowing how a computer chip is made and being able to make one are 2 fundamentally different things. Space-ready technology may be very widespread in 24th century but you probably won't be even able to randomly build your own fusion reactor, leave alone a whole military-grade fighter.
The only way to truely hurt the Terrans would be where there own interest would be threatend - like blowing up the shipyards that would've been gradually be rearranged to produce Terran parts or research groups that add to Terran science/R&D; but that would also deminish the Terran desire to keep them in existence in general.
#3b An PVE targeted for genocide would loose all inhibitions
They could not do anything about it if they'd loose their navy and GTA would drop a couple hundred Harbingers on their planet. It would not in Terran interest, though.
Right. But then, I still think the GTA would be at a technological disadvantage. The GTVA is fielding Shivan tech with the Kayser and with beam cannons, so they obviously did not bury all research. And although Bosch had high hopes for Etak, there's no saying that a more advanced version of the technology would help. It's not like things ended well for the NTF.
Despite the economic disruptions, scientific progress didn't halt as far as I can see that. As long as the Terrans not deliberately kill all Zod scientists, the outcome would be roughly the same.
We neither know whether the knowledge about the Shivans (or parts of it) was actually lost when GTI HQ was destroyed.