I wonder if it's possible. Don't get me wrong, France can be defeated harshly up to invasion (we have several examples, after all).
But SYW doesn't looks to be that of a war of annihilation, with each side being ready to reach a compromised peace, rather than push for too harsh terms that wouldn't be accepted and make necessary an even more important financial drain.
I'm not sure British politicians would be willing to pursue harsh terms, risking that France manage to get it better in Europe (Pitt previous tentatives of maritime invasion didn't played in favour of such plan); where they after all did a lot better than in Americas or India, or risking a Battle of Dinan reconstitution.
Would they risk Prussia to just say "nope" (too happy to make a favourable treaty similar to IOTL without risking another Austrian success), treat with Austria and France, and just eat pop-corn watching the ongoing war?
IOTL the Eastern powers signed their own peace treaty separate to Britain and France. Thus the Eastern powers can leave the war while Britain and France continue. The main reason the British gave an easy peace is that George III was worried about Pitt becoming too powerful. If George II doesn't die on time, Pitt could get the extra year at war, and control a much harsher peace. It wouldn't be annihilation, but it could be a bigger defeat, resulting in a smaller French navy, and enough to get Choiseul sacked.