Another approach - get some shoe sole rubber (It comes in sheets of varying thicknesses inc. 1/4") and glue it on to the bottom of the sole with 3M 5200. (Goggle 3M 5200 or West Marine; they carry it.) It is unlike any other glue so read the instructions carefully. It is expensive; probably $30 or more for a standard grease gun tube. Once opened, the whole tube cures in days; barely slower than the portion you applied as glue. Give it 3 or more days to set up.

This is a permanent fix. Boat builders use it to glue fiberglass decks to fiberglass hulls. Yes, they also go around and fasten with bolts every 6-8" but you can remove the bolts and pick the boat up by the deck. If there is failure, it will be the fiberglass, not the glue. I did this with two of my shoes that are MTB shoes but with the plate shim under the cleat, I was walking on just the cleat with that foot. Now the cleat just touches as I walk, but so does the other shoe. Footing is excellent.

I don't know where to send you to get sole rubber. Here in Portland I can get it from Oregon Leather. They might have an on-line presence. A cobble will certainly know but may well be unwilling to give up trade secrets. (He will however be willing to do the work. My first several pairs of cycling shoes were done by a local cobbler and his work was excellent.)