OOC : He said post 1776, so I imagine that the Iriquous are long irrelevant
BIC :
I can think of two things.
1: I think having Mexico gain independence later would be a problem. Perhaps the Machette Revolution *OTL failed, 1799* fail. With a weaker Mexico, who might get independence by 1830 or 40 as a Spanish dominion, more willing to secede land to the USA for rights or trade concessions as opposed to militaristic and expansionist one fighting over California and Louisiana?
2 : Perhaps have a better end of the war for the Americans? When the war ended in 1794 the British ended up boxing in America by holding everything west of the Mississippi and claiming Michigan plus seizing Louisiana and Florida. Maybe if the war ends earlier and the Americans don't let victories are Challinson, Yorktown, and Saratoga slip through their hands?
I think that decreasing Mexican and British Power in the Americas will lead a power Gap open for the USA to fill. There will be only a few wars, and we avoid the abolitionist secession of New England and constant border clases in southern Maine and Michigan between the British and USA, not to mention you have less internal strife in the largely multi-national tribal republics and maybe a less militant Mexico?
this of course makes things better for the USA, not sure how bad Mexico and the British will be.