What are some tips for fixing gaps between door and jamb in an exterior door?
Your plan to fix the gap in the center of the door sounds fine. I might suggest using some shingle shims instead of flat stock however.  If you want to just remove the interior trim only, that is fine also. Using the shingle shims, place the thickest end in first and by trial and error, adjust the opposing shim to a size that will snug in nicely and then by gently tapping it in next to the first shim, remove the excess gap. Put a small finish nail through the jamb and shims to prevent them from moving. Drilling a pilot hole will assure not splitting the shims with the nail in inserted. Now just trim off the excess and reinstall your trim.  Job done!    Good Luck