With a POD post 1776:
It's verging on ASB, but could we have a situation were Europe degenerates in a cycle of war and pestilence, getting so self-absorbed that there's no interest in American affairs, and, later, that depopulation is enough that there's lots of room for people to make new lives within Europe.
The *US still wants/needs settlers, and the only places with surplus people/energy are the lands of Islam (probably starting with North Africa).
Still going to be a problem getting a Muslim MAJORITY, 'tho.