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Okay, but the best theory, MWI, does not suggest different constants, and the theory that does is not particularly well thought of, am I understanding this right?
So, this is a bad rebuttal to the fine-tuning argument.
MWI is orthogonal to the question of different fundamental constants. MWI is just wavefunction realism plus no collapse plus 'that's OK'.
So, any quantum-governed system that generates local constants will do under MWI. The leading example of this would be String Theory.
MWI is important here because if only one branch is real, then you need to be just as lucky anyway - it doesn't help unless the mechanism makes an unusually high density of livable rules. That would be convenient, but also very improbable.