In a discussion on the Ballad-L list some time ago, Steve Gardham pointed out what appears to be an earlier form of the song; a broadside called The Banks of the River, where the stranger is not from America, but from Yarmouth, and his intended destination is Jamaica. Steve cited editions of 1802 (Robertson of Glasgow) and c.1800 (Angus of Newcastle), around 20 years prior to any known American Stranger texts. You can see a later edition (undated but post 1818) at Bodleian Library Broadside Ballads:

The banks of the river

Incidentally, re. Q's post of 10 April: I'm not sure where the Ballad Index's reference to The Irish Stranger as an alternative title came from (it is a completely different song) but it may derive from a comment in Gale Huntington's Songs the Whalemen Sang, which I think was an editorial mistake.