I went to HMS, and I can confirm that the mentorship and support are not particularly strong there. We had to be pretty self-reliant for everything.
Regarding reputation, for what you want to do, there will be absolutely no difference between Harvard and Yale. I think it's hard to see that as a pre-med, but I have personally witnessed it among my friends from HMS, Yale, Penn, Stanford, etc.
So, though I liked my experience at HMS, based on your list of factors, I would say that Yale should be your top choice, assuming the finances are similar.
Feel free to DM me with any questions.