I was trying to think of a Gettysburg thing, but my knowledge of the American War of Independence is somewhat limited.
You refer, sir, to the War of American Balkanization, or, since men from the Tate family fought on all three sides (including for Kentucky neutrality), The War Between the Tates.
Ahem. I'm fortunate enough to live 30 miles from Gettysburg and less than that from George Washington's choice for the US capital city: Wrightsville/Columbia, PA.
I think that Churchill wouldn't quit even if the Germans landed all 13 divisions without a loss and took the place. Now, if Halifax had been made PM instead - a highly likely alternative to Churchill and a man who had been in favor of appeasement but then recanted - and the BEF was bagged at Dunkirk, then a peace offer from Hitler/Hess might seem more attractive. Remember that Hitler was a favorite of many Britons of the time, especially the 'better sort' who thought him a good alternative to Communism. Not saying it's likely - but I doubt that Halifax would have been able to rally public opinion in the way that Churchill did.
The problem with using the Japanese fleet is that, in 1939, they're still hoping to consolidate China and stay out. Plus I think they didn't join the Axis until 1940, so that takes another bit of fiddling.
The problems with using the Italian fleet are fuel and resolve - the Italian light forces had resolve in spades but not their high command, and there was especially no desire to fight Britain.
The problem with using the French fleet is that, after the fall of France, there basically was no fleet in Axis or Vichy hands.
The problem with using the combined Axis fleets is that in the game, it is simple. But in war, nothing is more difficult than coalition warfare. None of those nations would accept another's admiral as an overall commander; it is doubtful, given the record of the Italian Navy, that they would co-operate with the Germans in any way. They'd need, at the least, a naval Eisenhower, and they weren't going to get one.
By the way, has anyone read the delightful, "The Red Napoleon" by Floyd Gibbons? It's a lost pot-boiler from 1929 assuming Stalin dies, someone more capable takes over and the Soviets steam-roller the West, ending in a climactic battle for Manhattan. Yes, that's right - the Mongols take Manhattan - but they can't keep it. Anyway, one of the central plot-points of the book is that Britain isn't conquered but falls to internal revolution and the new People's Navy is employed against the US. If you can get it as an e-book, do so - Gibbons was a seasoned war correspondent trying his hand at fiction and you'll be surprised how much of the militaria he gets right.
Now, this is just opinion, but I think RN losses at Crete, Malta and elsewhere would be acceptable if the choice was invasion. Britain could (and did) station light forces in Portsmouth and north of the Channel in places like Hull, running them in once the invasion starts. Twenty destroyers and a half-dozen cruisers plus 2-3 old battleships would not be difficult to assemble, and that's more than enough. German naval fighting ability in the Norway campaign was abysmal - even embarrassing.
And the trick is, you know how hard it is to keep men moving forward under fire? They try to go to ground or go sideways or back or anywhere except forward, even if they have more than enough numbers to swamp the defenders. It does no good to say, "If you go on, one in ten of you will get shot but if you freeze, one in six." Men do not want to advance into enemy firepower - hey, that one-in-ten guy might be ME.
Now apply that to a Channel crossing. The Zerstroyers are covering the barges and small ships, maybe a
Prinz Eugen is in the Channel. It's night, so the airplanes aren't attacking. Then
Rodney and
Warspite and six cruisers and a dozen DDs show up. Do the invaders go forward, knowing that half of them might make it?
No. The Army goes home and waits for the Navy and Luftwaffe to guarantee a safe passage - which never happens.