Well, after doing some Googling I downloaded a "recovery" program (Stellar Data Recovery) that seems to have a good online reputation. It's been running now for several hours. The "Preview" window shows intact files as well as the file structure so fingers crossed that this will do it.

If that doesn't work and I can't get the program to restore the files, I'll likely try the Microcenter route (or some data recovery place in SoCO. Maybe in the Springs?)