This looks like a very big "uh-oh" in the same type of error that has been the topic of several G2G posts since the recent privacy changes that we understand are legally necessary although create a great impedance to our work.
The other posts I have seen about this have all involved 1 open profile and 1 private profile being merged, where only the manager of the private one is able to complete the merge.
This one, however has 2 private profiles, so it appears the each of the managers has to be the one to complete the merge ... begging the question of how it is possible for 2 people to each be THE ONE person. Further complicating this is the fact that one of the two profiles is unlisted, so I don't know how the system will ever permit the normal merge action of both managers co-managing the resulting profile.
Carl, I think your best bet is to write to info@wikitree.com about this. You could also edit your question and add the tag: sysops that is likely to bring this question to their attention.