I have (had)the same foot problem. I bought leather sandals with a strap above the heel (not flippy ones) and with some side support, then super-glued in a Dr. Scholl's arch support I bought at
Walmart. These are 3/4 the length of the shoe. No one ever notices this! I did the same thing for a different pair that I use for houseslippers, since I never go without my arches being supported anymore.
The package says Heel Pain Relief Orthotics, but mentions right on the front of the pack that it's good for PF. Just super-glue these in, and you're good to go!