One, professor's realize that letters of recommendation are important and thus tend to spend a significantly greater amount of time and care in writing them.
Two, at least for my letters, my writers tended to ask either the committee, other prof's who'd had me, or my adviser to give them the once over for them. If he's a math professor, you could give him the info for your med adviser as a second pair of eyes/any questions on what to include/etc/thing. Don't outright say 'you're a ****ty writer,' but give them that option.
Three, yeah, a strong LOR is one from someone who knows you well, not someone who is a strong LOR writer with little idea of who you are or what you've done.