I don't actually know for sure that Jane 'S' is the same as Jane Burnham. But one of the marriage records to Jane Burnham does say Ben "Jr', the other doesn't. I couldn't find any children recorded closer to the 1808 marriage.
But from the census data that I noted previously, and additional censuses in that time frame in Maine,there were plenty of Ben Bailey's in ME of a similar age, with and without Jr etc.I think one was the son of an Andrew Bailey.
It would be easier for you if he was Hector or Herman, or just something less popular than Ben at that time.