But theory 2 predicts that Bob will probably vanish!
I don't think it does. The probability current is locally conserved. So |u'> has to give a high probability to some world very close to Bob's, i.e. one with a continuous evolution of him in it.
Hm, so you're saying that if |u> has high probability density in the subspace that contains Bob, then in the near future there must still be high probability density there, or at least nearby. But in fact |u> has very low probability density in Bob's Everett branch. Consider all the accidents of weather and history that led to Bob's birth, not to mention the quantum fluctuations that led to Bob's galaxy being created.
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.