I am also in the same situation, interview is in the 1st week of April and can't manage to have an appointment for the medical examination before. one doctor said may 10 and the other April 24th, and one doctor just does not answer.
one doctor said no problem for the passport as long as you bring a certified copy (copie légalisée), check with the doctor if this is a possibility as well, so you don't have to ask them to return your passeport ( our lawyer said not to ask for passport back and simply mail the medical report to the consulate when it's ready).
we are really stressing because of this and hate to be put in AP because they can't coordinate appointments with their fully booked doctors.
please let us know next week after your interview how things go, what they say about not having the medical done and what they do about the passport? good luck