First, since this post has blossomed into quite the

of text, the TLDR version: conquering Sol will do little to solve the problems that drove the GTVA to invade in the first place. Win or lose in Sol, rebellion and collapse are seriously likely.
The following exchange in the WiH Census thread got me thinking about the GTVA’s options at this point.
I don't really want to get into a point-by-point argument so I'll just say that
I think you're oversimplifying the problem here. It's not just that 'something will happen which will destabilize the GTVA', it's that almost all outcomes destabilize the GTVA.
Don't finish the gate? Population rebels at broken promises.
Finish the gate, don't declare war, don't try to control immigration? Enormous emigration to Sol.
Finish the gate, deny immigration? Rebellion that makes the NTF look like a picnic.
Finish the gate, attempt diplomatic resolution and staged immigration? Ubuntu ideology spreads virally.
Think of the GTVA in that situation as East Germany and the UEF as the West, except East Germany believes it needs to exist to keep the West safe, and the West doesn't seem to care much about that at all.
Ah but I can add to that:
finish the gate, have war, win war, deny immigration and still face just as large a rebellion on your side AND face rebellion/unrest in the recently conquered Sol system.
So, the war having started, let’s looks at the various ways (some much more likely than others), in which things could pan out. We’ll work our way from UEF victory to GTVA victory.
Scenario 1: Total UEF victory. The UEF routes GTVA forces in Sol, pushes through the node to Delta Serpentis, and proceeds to sweep through the GTVA system by system. The Security Council is either killed or signs an unconditional surrender at gunpoint. This would practically require direct divine intervention on the side of the UEF, but this being BP that’s not exactly outside the realm of possibility.
Result: the GTVA is conquered. The UEF may or may not actually disband the military/put the Admiralty in reeducation camps where they’re forced to learn Linux/turn the GTVA’s daughters into bloodthirsty pot-smoking schizophrenic lesbians/whatever the hell else the Security Council is afraid of, but in any case its curtains for the GTVA.
Scenario 2: Limited UEF victory. The UEF destroys or routes GTVA forces in Sol and reclaims their greatest advantage in this war: the ability to concentrate their defenses at a single subspace node. The GTVA gives up.
Result: The defecation hits the ventilation back home. The population accuses the Security Council of not taking the war seriously given the relatively small fraction of GTVA forces committed to Sol. Whether the accusation if fair or not, it’s enough to lead to rebellion. If the rebel forces are victorious, Possibly see a slight modification of Scenario 5. If the GTVA is victorious, well good for them, but they’ve taken severe losses and Sol is still blockaded (and probably has a lot more destroyers by the time the GTVA has cleaned up its mess at home). Depending on what sort of mood the UEF is in at the time, Scenario 1 becomes a possibility again.
Scenario 3: Truce. The UEF and GTVA fight to a draw.
Result: Pretty much the same as in Scenario 2, although if the rebels win then they’re probably in a better position to attack Sol.
Scenario 4: Quagmire. The war stagnates, and the GTVA forces in Sol are in no danger of defeat but fail to achieve victory.
Result: Again, questions are raised about how seriously the GTVA takes this war, and somebody stages a coup on the platform of committing more forces.
Scenario 5: Pyrrhic GTVA victory. The UEF destroys or routes GTVA forces in Sol and reclaims their greatest advantage in this war: the ability to concentrate their defenses at a single subspace node. The GTVA, faced with certain rebellion should they walk away from the war, commits everything.
Result: Easily the stupidest thing the GTVA could do. The entire GTVA fleet pours through the jumpgate in single file, straight into the waiting guns of four destroyers and numerous frigates. They eventually prevail given their vast numeric advantage, but the losses are appalling. Unless the GTVA is really lucky, somebody is probably going to use this as an excuse to stage a rebellion, on top of that. And that’s assuming the Shivans don’t show up before the GTVA can replenish its strength (a matter of years, if not decades).
Scenario 5: GTVA victory by UEF surrender. Pretty straightforward. The war keeps going the way it has been, and the Elders surrender.
Result: The GTVA now has to deal with exactly the same problems as it would have had it left Sol alone. If people wanted to migrate back to Earth before, they still will now. Ubuntu is still present and widely practiced on Earth, even if it no longer forms the basis of government, and the danger of its spreading remains. This danger is made all the more real because the harder the GTVA tries to repress Ubuntu, the more they will justify its ideology. On top of that, at least some elements of the Second and Third are likely to ignore the order to surrender. If they take either the Bretonnia or Solace back from the Elders in the process of going rogue, they could wreak havoc in the Sol system for years.
Scenario 6: GTVA victory by UEF surrender, followed by GTVA restrictions on migration back to Sol.
Result: Crazy Dave already covered this. Can you say ‘rebellion’? Yeah, I thought so. Plus the same problems with remaining elements of the Second and Third as listed in Scenario 6.
Scenario 7: GTVA victory by UEF surrender, followed by the eradication of Ubuntu, after which immigration is permitted. The GTVA is going to have to turn the entire system into a reeducation camp, and a full-blown police state replete with death squads is equally necessary.
Result: And, if it’s possible at all, it will take a LONG time. Long enough that the GTVA’s nascent population of proto-rebels will get impatient and go for the throat. On the plus side, GTVA forces would at least get some cool new black uniforms out of it.
Scenario 8: GTVA victory by total war. The UEF fights to the last man, and the GTVA incinerates every inhabited surface in the Sol system.
Result: Well, nobody wants to move back to Sol anymore, but they’re probably kind of pissed at the GTVA for expending massive resources to go back to Earth, only to go Vasuda Prime on it. This is not going to help stability. Not to mention the fact that if the GTVA mounts attacks this direct, they’re probably going to lose at least a destroyer or two before the UEF fleet is destroyed.
And all of these ignore the possibility that Steele may have already started TVW2.
Anybody have a scenario in which the GTVA is not completely and utterly screwed? Or am I completely mis-thinking one or more of these? Because the best option for the GTVA at this point seems to be to fly around their wing of Maras in Sol a bit, scream bloody murder about a third Shivan incursion, pull the fleet out, M-bomb the node, and hope nobody calls them on it.