Hi Dave,
the system needs around 4.0V minimum for reasons other than the PIC itself, also the PIC will be doing a low battery detect with the on board PLVD module which is internally tied to VDD, so an extra diode drop will mess with the limited trip points available

i sort of suspect there must be a lot of PIC systems using a series diode and 4 alkalines which are in the same boat

BTW, a regulator is not an option either due to the requirement of several uA standby
oh and did i mention the board is about 0.8 inches sq with about 25 parts including a sw reg?
so frankly i am not sure i could even fit another diode