Without Washington taking an active role in politics, Hamilton would not have been as influential as he was. It's doubtful Jay would have included Hamilton in his cabinet. Hamilton is either serving in the House or back in New York in this timeline.
I was thinking House, though I have no idea what district.
Most likely the 2nd District. I don't have access to a district map, but none of the other five districts of the original six were represented by Manhattanites.
However, assuming the electoral history of New York is even remotely similar, Hamilton would have to compete with John Laurance for that seat and quite possibly lose. Without knowledge of what Hamilton might be capable of, I'd probably vote for Laurance, the judge who sentenced Major Andre to hang, over the banker Hamilton.
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