Wow. I don't think I've ever stumped Usenet before. No worries, I
figured it out. The solution was embarrassingly simple, natch:

Application.DisplayAlerts = False
With NewWkbk
.SaveAs Filename:=SavePath, FileFormat:=-4143, CreateBackup:=False
.Close SaveChanges:=False
End With
Application.DisplayAlerts = True

Got all fixated on the CheckCompatibility property that I just forgot
about good ol' DisplayAlerts...

..o.