Personally I'd say the MD degree trumps the MS degree. I don't know that they'd grant a deferral just so you could finish.
On a side note, I know a handful of people who have completed their theses in medical school (over the summer if needed). One of my classmates even defended his PhD dissertation.
Yep schools require such letter either from the chair of the grad department or the graduate supervisor but most schools have no mention of graduate requirements what so ever.
I am assuming that if they needed such letter they would mention it.
I will still get my PI to mention it (if she agrees) and send the LOR to all schools (will exceed the limit at many places but I guess it should be fine as I have a legit reason).