I don't totally disagree Mr. V, but ...
"... selectively transferring a subset of courses between instances."
Auto backup not good for 'subset of courses' - with auto is more an all that match options (and moodle routine for this can't do Vulcan Mind Melds with op). If site has been using auto already, might have to start with a clean slate of related tables by truncating them all, then run auto ...
depending upon what Op means by 'subset'.
One will end up with a bunch of courses in one directory and 'un-organized' as to 'subset' (whatever that means). That equates to more work on the new server rebuilding.
Again ... my 2 cents!