You could have submitted medical with initial packet and not wait for RFE...
Did you do biometrics already?
The problem is, OP has to send the old passport back now. Based on the news from the UK, it will take a while to get the new passport.
@ljatw1 have you explored getting an emergency passport? Are you eligible for one? Maybe it could serve as temporary proof of ID. For medical, UK driver's license should be OK. But for biometrics appointment - do not remember, but they ask about nationality.