Kind reader Sheri reminded me of an excellent invisible zipper tutorial, so I decided to rip out the dress's zipper and try re-inserting it using an invisible zipper foot. I was worried that I wouldn't be able to because all of tutorials I've seen indicate that an invisible zipper should be inserted before the seams are sewn.
Despite that the dress was already constructed, the zipper went in relatively easily. It looks soooo much better. No zipper tape to be seen, and only the little zipper pull is visible at the top.
So even when a dress calls for a regular zipper with topstitching (as this one did), I still think I'll try to insert an invisible zipper, but before the skirt lining is sewn in.