I did say strong arm.They are willing to pay a compensation for Bavaria's troubles,with Hanover.As for annexing a place without a claim or reason,look at the Polish-Lithuanian Commonwealth.
About East Prussia,what if the Russians exchange that for Courland like others suggested?Brandenburg will probably be irrelevant to them if this happens right?
The first partition of Poland was justified by Polish civil wars and anarchy, to "restore order" to a troublesome neighbour. Bavaria has nothing equivalent. If they did this, I can really see a British-Russian alliance, backed by smaller powers, that would be very hostile to France and Austria.
As for the Russians, I don't believe they would swap Courland for Brandenburg. People saying that seem to be treating Poland as an independent power, and that Russia would want territorial contiguity. Actually, Russia would like to have a good reason to be marching troops back and forth through Poland, as it keeps Poland as a more compliant vassal. East Prussia also gives better power projection into central Europe.
The more I think about it, Saxony could be the answer:
1) Austrian Netherlands to France
2) Saxony and Silesia to Austria, with rights guaranteed for Protestants
3) East Prussia and Pomerania to Russia to keep them happy
4) Hannover to the Wettins, with bribes
5) Sweden screwed, but hey, they didn't contribute much
6) Britain with lots of new colonies