How can genealogical sole-progenitorship be supported? It’s even more impossible than genetic sole-progenitorship, which is at least theoretically possible given a miracle of coalescence. And in fact genealogical sole-progenitorship would entail genetic sole-progenitorship, though the reverse is not true. You have lots of genealogical ancestors at any time-period, lots more than you have genetic ancestors, as you yourself have demonstrated. Unless you mean something by “sole” other than sole, this doesn’t work at all.
Have you forgotten the MHC alleles already?