I had a similar RB problem - gummed up shutter.
Since the shutter is in the lens, all exposures were the time from mirror up to re-cocking the shutter. Don't know how the RZ works regarding mirror and recocking, but the only issue I've had in about 2 decades of RB shooting is one lens with a stuck shutter (cleaned up and back in action). I understand the RZ shutters are much cheaper, more plastic parts, more failure-prone - got any access to another lens?