wheel not fitting?

sounds like it
(i wish i had the car here, so i could see)
would this press the outside of the drum down unto the backing plate?

Oh yea it could.
Drums are made to have the front plate of them flat against the hub and pinched between the hub and wheel.
They are actually very thin, so if the rim inner diameter is contacting the drum before the drum is pinched then it will push the outer part of the drum into the backing plate.