I found myself thinking that the strong sense of rhythm in USA folk versions of British originals must have come from African influences

I doubt the US and UK evolved all that differently. Military culture has always been a huge presence in the US (and still is, to an extent unimaginable here - who has ever heard of a kid being sent to a "military academy" in the UK?). The early jazz musicians were military trained and used military instruments, and fife bands survived into the middle of the 20th century when Bayard researched them in western Pennsylvania - their idiom was not that different from the Irish or Scottish sectarian flute band style. African-American musicians can't have been immune to influence from military music of European origin.

Quite possibly Irish music was more similar in this respect than is generally recognized. My great-grandfather was a peasant from Mayo who joined the British Army at 14 and learned to play the flute in Afghanistan; there wasn't anything extraordinary about this. The British Army was where almost all flutes used in Irish music came from. Military rhythms must have influenced Irish dance music rhythms.