Surely "science" as a method is indifferent to interpretations with no observable differences.

Your point seems to be that "science" as a social phenomenon resists new untestable interpretations. Scientists will wander all over the place in unmappable territory (despite your assertion that "science" rejects MWI, it doesn't look like that to me).

If Bayesianism trumps science only in circumstances where there are no possible testable consequences, that's a pretty weak reason to care, and a very long tortured argument to achieve so little.