[doubleunplussed]

The main thing that's wrong is that we have no reason to believe the fundamental constants change.

Regular quantum mechanics is compatible with the many-worlds interpretation (of course it is), but talk of fundamental constants changing would require new theories that we don't have (not to mention evidence of those theories). That would be something incompatible with quantum mechanics as we know it, within which the fundamental constants are, well, constant.

[rantwasp]

just because those constants are incompatible with our current understanding does not mean it's not possible, even if only on a theoretical level.