Sure, I used the word 'theory' incorrectly, I should have said 'explanation'.
As I understand it, hidden variables are fine if you're happy to throw away locality, which is exactly what Bohm interpretation does and exactly what we're talking about here.
Since your analogy is purportedly showing me how MWI is local, showing me that something that is significantly different (i.e. is a hidden variable explanation) is also local doesn't help a lot.
The Bohm Interpretation is the experimentally indistinguishable dual of MWI that proposes hidden variables rather than the absence of wave collapse.
Despite the hidden variables in the Bohm Interpretation, there is nothing wrong with it, modulo Occam's razor.