The best way for the US to succeed as a superpower is to not leave the Empire in the first place. The problem there is that far too much credit is given to the rebels (who wanted it) for the separation. Not enough
discredit was given to a Whitehall and Parliament that had clearly not sufficiently evolved by the end of the Seven Years War to properly administer a set of American Colonies that had outgrown the outdated forms of administration that was still quite suitable for remote island/port colonies.
Dominion Status (I) would have saved the day, but there was no possibility that men like Lord North or Mad King George III would have ever accepted such a profoundly British

(and modern!) idea.
By the time Britain's hand was forced to the point of considering such options, not only was blood being shed on a massive scale, but the French had already entered the war, rendering the idea of a peaceful settlement with America as a British Possession moot.
If the American Colonies gets Dominion Status post-1763 (if such a thing had been politically possible-DAMN rotten boroughs!), then
SergeantHeretic's suggested TL may not be so fantastic after all.
However, I would caution against any silly British hyper-hyper-power scenarios, as has been seen in ATL fiction. The American Colonies, even as a Dominion, would have gone their own way eventually. Just like Canada, and perhaps one day Australia and New Zealand. And if our own history is any clue, I doubt seriously we would be seeing American troops fighting under Wellington (the Dominions have GENERALLY had a history of engaging in serious Imperial support in campaigns where their OWN interests have at least SOME applications; save Australia and New Zealand, that is).
Most likely, as an Imperial Dominion, the Americans would simply follow a pathway like that suggested by SergeantHeretic, or comparable to the westward migrations of the Canadians, the westward/northward migrations of the Australians, and the northward migrations of the South Africans.
I) In all seriousness, I would have to say the idea of our leaders in 1763 coming up with Dominion Status (and not being promptly laughed out of politics) is ASB.