I’m not worrying about the mathematics. If there’s a problem there, it is with the physics (including the mathematical modeling) rather than with the mathematics. But physicists are well aware that quantum particles don’t fit our classical mathematical models.
I expect this doesn’t actually show that something really strange is necessarily going on here, in that I have a rough idea of how Bohmian mechanics could explain the result of a similar non-relativistic experiment without any weird contradictions.
It comes down to the fact that “measuring whether two particles are in the same box” is not the same thing as measuring the position of both particles and comparing them; it may in fact correspond to an experimental intervention that doesn’t (from a Bohmian perspective) accurately reveal the pre-measurement particle positions, because the experiment itself influences what those positions are.