Just my 2 cents. First take a bunch of pictures of the radiator so that you or the shop (if needed to hold someone accountable) can refresh their memory of the details. Which strap is on which side, rod location and other things. Since your not going to need to strip the core (what a pain for many ) the task is not that much a a problem. You can use some aircraft stripper for the task. After talking first see if they are ok with you disassembling the radiator (side straps from the rest and top or bottom tank if those need any work), restoring the surfaces and then supplying those parts back to the shop for core replacement and reassembly. You can specify that they leave it unpainted so that you can do that task if you choose.
Don't expect that a shop will care or have any idea of how to restore your radiator. That is not their typical job. Good luck finding a core as this has been the biggest challenge for many since many look very different from originals. Ask to see one and compare for yourself
There are a number of threads on the paint, process and the results of heat cycles on the finish - on this site.
Good luck with your project