How might we find people who would be willing to devote 30-40 years of their professional lives to living in a hick town and serving the people there? What sort of people should we be looking at? What questions should we be asking? Who's going to deliver the babies, take care of the old folks with heart failure and treat the kids with asthma?
As someone who spent many years growing up in a "hick town," I would suggest recruiting the "hicks" who have family ties to the area. A lot of these places in the middle of yonder are family towns with populations of less than 2000 people (per town) where everyone's grandpa knows everyone's grandpa - and can recite family histories of a good portion of the town (since most town's residents have several generations of family members in the area). These people often times want to stay near their extended families, cousins, childhood friends, etc. But some of them would probably be open to leaving for a few years to become a doctor and later come back to serve their own community. (Much different than an outsider moving in, who may not feel the same degree of connection to the place.)
The only caveat, as I see it, is that a recruiter would have to go to their high schools. Many "hicks" aren't comfortable navigating the "big city" - especially the parents. They may be wary of new things and new people. A non-threatening recruiter with a clear-cut simple plan (easy to understand) might do the trick. The best program, I think, would be an undergrad/medical school combined program where they could go for a few years, and return home (again keeping things simple and clear). New people, fine print, complicated matters, uncertainty, all risk losing trust*.
I suspect that the first person from a specific super tiny, isolated, and poor community to go to medical school as part of a recruitment program at the local high school would probably make the newspaper. Then everyone would hear about it. The local who finished the program would essentially be famous for it locally. They would be asked about it. And the locals trust their own.
The trick to getting them to go back and serve their community is to pick people with strong family ties to the area, who prioritize living near their family.
All of this is based on my experience on the countryside. Surely there are many countrysides, and some may be different.
*Edit: A way to build credibility beforehand (ahead of a recruiter) would be to send an announcement to the local newspaper explaining your program, a short history of it, the purpose of it (so it's plausible rather than "too good to be true," and maybe how it works. The credibility of the press in a small town can work wonders! (Even though your program is likely prominent, some "hick towns" don't follow medical school rankings, or for that matter even the basics of college sometimes. They might need to be informed.)