I have a 1957 CJ5 that is primarily used as a hunting vehicle in South Texas that is needing a new paint job and minor body work. For decades we have simply grabbed some cans off the shelf to patch it up.

Most shops don't want to mess with it as I'm not requesting show room quality, just smoothing out a few of the major dents from years of use, blasting the previous decades of paint, and finishing with a new primer and coat.

Does anyone have any recommendations on local shops or individuals that may have experience with this type of request in the area?

If it is already in South Texas you can give these guys a holler. I have watched as their business has expanded:
Sanchez Auto Repair

Arredondo's in Hondo. Its just south of Hermann Sons on the side of the overpass and in the same yard as the towing place. They will be exactly what you're looking for.