you might find more information referencing cross-domain with GA in
google groups, since this is a DTM forum and your adobe setup seems to
be working.. not sure what the question is. I don't believe there's
anything dtm or adobe analytics can do to help with how GA records
visitors. personally i wouldn't piggy back either platform on each
other. if you need both, then run them in parallel, but understand that
tracking will always behave slightly differently.