Tim, I thought there was only one "shut up and calculate" interpretation, and that's the one where you shut up and calculate - rather than talking about many worlds. Perhaps you mean it's a "talk rather than calculate" interpretation?

Suppose I announce the Turtles-All-The-Way-Down "interpretation" of quantum mechanics, is it fair to say that the TATWDI "makes the same predictions" if I can't actually show how to get a number or two out of this postulated tower of turtles, but just say it's a way of thinking about QM? If MWI makes predictions, show me how it does it.