this is more of a question on american thinking. in early 1942, the US already had a strategy for fighting both japan and germany without britain and the soviet union. that's why they focused on europe first and let bataan fall. they had to beat germany before it knocked out both britain and russia. what's important to note is the US never stood by and just let other countries seize the rest of the world.

both sides already had designs for a trans-atlantic bomber as of 1944 (although i doubt if they can carry a-bombs shore-to-shore.)

the US can develop a trans-oceanic navy faster than the germans can. we'll assume the german navy has been sapped to the limit on invading britain. britain, meanwhile, would have transferred it remaining naval units to canada, india and australia.

the fight will happen in the middle east, north africa, india, china, indochina, and possibly south america. more likely, just as the US had with the USSR, both sides will wage proxy wars in these regions until one side calls it quits.