Their positions weren't totally cynical -- John George clearly wanted to be loyal to the emperor, but events spiralled out of his control and at times he ended up in rebellion anyway. To answer your question, his actions during the war suggest that he wouldn't desert the Swedes at a time that would provoke a Swedish invasion of Saxony when it had no ally strong enough to fight off the Swedes, but might do if the opportunity presented itself. If Gustavus thinks a Saxon alliance is worth it, he could grant Saxony some rich territory from Bohemia (maybe Silesia), so that it would be hard to go back to the Hapsburg side.
Excellent! Thanks for the answer. The only problem with granting them Silesia is that Bohemia would not like its territory partitioned (This was one of the reasons why Frederick, Count of Pfalz, failed to get Saxony on his side - the Bohemians would not allow Lusatia to be given away to Saxony). But maybe, if Gustavus is successful, he can buy the cooperation of Saxony with some of Frederick's lands in Julich-Berg (or was it, Mark? - I don't remember offhand). Anyway, ITTL, with the defeat of the Bohemians earlier in the war, they may not be as able to protest as effectively as they did against Frederick.
However it plays out, one day the Germans are going to resent having a foreign ruler.
This is a given. Sweden's role in the Protestant Union is going to be less smooth than Austria's rule was in the HRE.
Protestant Union: No problem.
Loss of Bohemia: Painful, but without the ability to resist, I think the Hapsburgs would have to fold. By this time, however, the Bohemian protestants had been expelled so imposing Frederick V or another Swedish candidate would be a traumatic procedure. Which goes to your last point about whether Sweden would still have a need for French gold.
Loss of Austria: They'd never agree. The Hapsburgs would just go into exile and hope that their Spanish relatives could take the lead in restoring them.
Very good. We can take it as a working hypothesis then, that in the event of Swedish victory, most of northern Germany, including some moderately powerful states like Brandenburg, Pfalz, Bohemia and Saxony have been integrated in the Protestant Union, under the tutelage of Sweden (which would grab as much of the Baltic coast as it could get away with). Habsburgs retain Austria, Tyrol, Styria and parts of Swabia, and maybe even Alsace.
Dissolution of HRE: I suppose it could happen but I'm not sure anyone wanted that outcome. Ferdinand II was in late middle age by this stage, so he could be allowed to live out his reign. Given the disaster his reign had turned into, it's reasonably likely that a non-Hapsburg could be elected after he died.
It is not so much a case of Sweden disbanding the HRE, as the secession of most of Germany rendering its end an inevitability. This is like the Confederation of the Rhine come two centuries earlier. The Italian states were all Spain's backyard (Milan, Tuscany, and Naples, at least, were fully in the hands of the Spaniards). With Austria crippled, there is no HRE state capable of protecting the interests of the Catholics against the Swedes and the Protestant Union. Further, with Austria so badly weakened, I cannot see the Hungarians wanting a Habsburg ruler in this case (will they offer the crown to Maximilian of Bavaria?) I can easily see the Catholic remainder of Germany gravitating towards France or Spain (with Bavaria playing a vital role) in creating a Catholic League to protect the interests of the Catholics. Whether the Spanish Habsburgs will have much credibility left, with Habsburg defeats of this magnitude is, of course, open to question.