I was looking up the
Medical Scholars Program at U Illinois, but they are saying they're not taking students.
Their website said it was due to the formation of the Carle SOM program, so that's off the board. (I appreciate you forcing me to recheck my homework and links to this program.)
AAMC does have a page on this question:
MD-PhD in the Social Sciences or Humanities: Is it Right for Me? and it appears there is a directory
MD-PhD in Social Sciences or Humanities and Other Non-Traditional Fields of Graduate Study . Hopefully that directory is up-to-date.
Now to actually try to make suggestions to the question...
Every MSTP program should have a policy on taking LOA. I also think every medical school will have a policy on taking LOA for research though not sure for PhD (that really disrupts your timeline to graduate).
I would also check whether there are faculty that have appointments both in the medical school and in the desired non-med school department. The more there are, the more likely you may be successful. Reach out to them to set up a chat to talk about your plans and whether they think their school is the right place for you to fulfill them. The smaller the medical school faculty size, the more likely that the person you talk to may be involved somehow in admissions (interviewing at least), but chances are they don't really participate much in file discussions so they can really give you honest advice.
I will also encourage you: it's okay to get your Ph.D. first and do it the "old-fashioned way."