Hey, not done with my epi mph yet so not really familiar with all the options out there since I'm planning to go to medical school when I'm done as well.
I do have an idea you might want to look into that bridges some things you mentioned. You talk about being burnt out on the research process and wanting to do something more patient centered and have more interactions with the hospital system and physicians, but that having papers might be helpful to the application process as well.
For my field experience I deviated a bit from the usual gigs where people do data analysis for a non-profit, do a project abroad, work at the local health dept etc. I think they could have been great opps, but knowing I wanted to do academics most likely down the road, I opted to do some clinical research that would also get me exposure to physicians practicing medicine, patient interaction, and utilize a bit of my epi training. No lit reviews or meta-analysis required.
Basically I got a volunteer gig as a research associate in an ED. The dept. generally has about a dozen different studies going on and uses pre-meds, med students, grad students to screen patients to see if they qualify for any of the studies, talk to patients and get informed consent if they want to participate, then do data collection appropriate to the study (ranges from vitals while the patient is being intubated, to recording drugs administered by docs, asking patients a series of questions, doing observations), then doing chart reviews and so forth.
So I got to see the docs doing lots of cool stuff, got to see patients in all of their states from sick to drug seeking to critically injured to drunk and being violent and restrained. They also had some interesting conferences I got to attend and a few talks about getting into medical school. I'm not doing it over the summer, but I really enjoyed it and hope to start again in the fall if my schedule permits.
My position was volunteer and geared towards pre-meds with a bit more responsibility for med and grad students. However, opportunities like this exist that are paid. Your training in epi isn't exactly in clinical research, but you might be able land a clinical research coordinator or related position at a hospital doing similar work since you have some study design experience. It'll give you patient interaction usually but not overdo the stuff you seem burned out on.
It could give you the option to publish and get you more direct experience with the healthcare system. Otherwise, what about doing more applied, less research oriented epi like doing outbreak investigations or working for a non-profit?