I disagree with several things here, no offense (a larger Seven Year's War is interesting)
Augustus III, ruler of Commonwealth. One problem. He is also Elector of Saxony... which fought against Prussia and lost badly. ...
So yeah. OTL was IMHO best case for Britain-Prussia. They got a couple extra allies, INSANE luck in regards to Russia, and stunning colonial victories. Any change and they are screwed. They don't call it "Miracle of the House of Brandenburg" for nothing.

By all expectations looking from a present-day perspective, Prussia should have been crushed. With defeat on the continent, Britain will not be very happy. A larger Seven Year's War, such as the involvement of Polish forces against Prussia as well as Saxon can only make it worse.
Again, I like the idea, but I cannot see some of those countries joining and having those impacts.