While the idea of a monarchial America under the Washingtons is enduring and entertaining, it's very unrealistic. Thus, I've labored to make a TL of this idea, with a more plausible POD than Washington becoming king after the Revolutionary War. It is thus:
A more successful Shays' Rebellion leads to an abortive Constitutional Convention, which ultimately ends in the reinstatement of the Articles of Confederation. Washington, and Hamilton, his new ally, believe that America needs more centralized leadership, and thus, the Federal (Empire?) of America is created, with a Jefferson-led Republic of America seceding soon afterwards.
I'm aware that it's still a bit implausible, so any suggestions to make it less so would be very much appreciated.
I have a lot of notes, if you're interested.