It turns out that the source of many of John Wright III's children, and also the ridiculous number of children that his eldest son James has, is a set of bad merges. Here's the most recent one:
https://www.geni.com/merge/view?revision_id=72555756770
It looks like the merge was attempted because of a *previous* questionable merge, where another copy of the "correct" James from North Carolina was merged into the other James from Virginia, which made it appear like there were a number of children in common.
Sigh.
I think the best thing to do is try to undo these merges one at a time, until we get back separated families. Alternatively, I can try to split James, but that won't do anything for father John, and I'd have to split him too and recreate that part of the tree from other sources. Erica, what's your best advice?