@dreadnought jenkins:
Before moving on to the War of Bavarian succession how about Peter 3. war on Denmark-Norway to regain his family possessions in Slesvig-Holstein? Or is be deposed off before he can bring any such schemes alive?
Well Elizabeth will live long enough to see the treaty through to its end, and so after the partition takes place, I would think the Russians withdraw from Prussia through Poland.
From there, I'd maybe see things go like this:
Peter doesn't have any troops on the ground near Denmark, so he either has to land the troops by see, or negotiate passage through Poland and Prussia.
Meanwhile, Catherine, concerned that Peter's growing relationship with his mistress will result in her divorce, tries to stage a coup against her husband.
Since the Seven Years War went well, there isn't so much discontent and someone rats her out.
This distracts Peter for a little bit, and he sends her off to a cloister and begins making moves for his divorce.
This probably would have to correlate at some point with the Polish election so as to ensure Sigismund II August military coup never happens.
Anyway, his proposed war against the Danes is still unpopular, and wether he tries the naval route or not, I'd assume the Common fleet is the better of the two baltic fleets and would score some victories at sea destablising any supply lines.
Into this unpopularity, Catherine escapes her imprisonment and with far more support, stages a succesfull coup.
The war against Denmark-Norway is then called off, with maybe some minor reperations going to Copenhagen to smooth things over.
I havent given it any though before due to lack of information, but now that you've mentioned it it might be interesting.
As someone mentioned earlier, it probably would be easier if Quebec/Ontario was returned to France, in exchange for Hannover being left alone.
This of course would leave the Americans with a continous French threat to the north and a British Parliament wishing to make the Americans pay their share of the war.
If this was the case, I'd see popular support for indpendence drop while the two sides eventually work out some kind of deal.
Maybe a revolt by some more ardent Patriots, but without French support or even popular support, it gets crushed. This convinces London that something should be done.
Anyway, the American Revolutionary War gets butterflied, and we need to start looking for a new global war and Britain is smarting.
Now for a change, Catherines plot fails. Seeing this, Peter III puts his plans for regaining his old familly lands on the back burner and spends some years putting his house in order reforming the Leib guards and other social and government practices.
Denmark-Norway is not ignorant of Peter's desires, and spends some time making friends.
Eventually, a decade or so later with Catherine fully divorced and in some god forsaken part of the empire, Peter moves against Denmark-Norway.
How any alliance would play out I'm not sure, but Britain has and always come out on the side opposite of France.
This is all just thoughts and possibilies, so hmmmmmm