Einstein was actually against what is now termed "objective collapse" models, not Bohr's "shut up and calculate". And yes, the hints are increasingly pointing toward something along the lines of RQM.

Einstein was perfectly right about a correct physics containing no randomness

Maybe you should try playing your own rationalist's taboo with the term "randomness". For example, if you define it instrumentally as inability to predict an outcome of a measurement, then it trivially goes through in the MWI model. What's your definition?

no mysteriously-non-communicating FTL influences

Try similarly tabooing "influence". It is likely that you will find that "non-communicating influence" is devoid of meaning (it's a piece of logic disconnected from physics, using your favorite duality).