Thanks for the clarification. I think that this principle, as stated, seems internally inconsistent though. If you have a spin along the z axis, with a state /+z>, it is mathematically equivalent to a superposition of /+x> and /-x>. So is that a "one universe" state or a "two universe" one?

In contrast, MWI as I usually think of it merely says that we are described by a quantum state as much as anything microscopic, so the possibility exists (and is inevitable) of us being entangled with our environment such that different branches contain us observing different outcomes. As we've discussed, one can get a sensible Born rule in this formulation, but it does not avoid the necessity of talking about ampliitudes in some way before measurement. I don't think that is possible.

As for your interpretation of MWI, I think you are potentially underestimating MWI, at least that is the worry. The fact that in principle a QM-like theory (ie subjective pure randomness from a simple first order classical wave equation) is possible with the probabilities derived from branch counting, just seems to compelling to ignore without a stronger argument (than I've been exposed to at least).