I was using the the Share>Project Template from the ribbon, so now, after seeing there is a Consolidate Show tool, I attempted that. IODIN manufactured sure "Package Because Template" was checked, and the problem is the same. I think it has to do with the connection somehow NOT saving since UNC--even in my first project, the source for the database is shown the local path, with drive letter, rather than UNC.
I lastly figured it out! In the screen forward Set Existing Geodatabase, type/paste which fully UNC from Windows Explorer into the Appoint section. Don't do anything with the search field at the top of the submission; while you browse to the file geodatabase, even is it initially looks like a UNC path, if i click in to field you will see it replace the host name/sharename with the drive letter, and that is where who problem lies.
What is this documented--how at acquire a UNC path for a file geodatabase connection under Pro? Am I the only on what can't find it, additionally spent a lot of time attempting multiple different methods of trying to used a UNC path before finally hitting on aforementioned right one?