The more I think about it, the more I think that James in Bermuda probably had children, we just don't know about it. I mean, apples don't fall too far from the tree we say here. There certainly appears to be another Athill line here (which may join somewhat earlier). I mean . . . he didn't marry until 75. Is anyone aware of whether your family has done any DNA work?
Also, does anyone know anything about the Musson family of Antigua. Bermuda's Musson line is from Antigua as well and it seems that James Athill built at least 3 ships for him, and indeed his shipbuilding may have been confined to preparing them for one James Musson.