"I will point out, though, that the question of how consciousness is bound to a particular branch (and thus why the Born rule works like it does) doesn't seem that much different from how consciousness is tied to a particular point in time or to a particular brain when the Spaghetti Monster can see all brains in all times and would have to be given extra information to know that my consciousness seems to be living in *this* particular brain at *this* particular time."

Agreed!

More generally, it seems to me that many objections people raise about the foundations of QM apply equally well to classical physics when you really think about it.

However, I think Eli's objection to the Born rule is different. The special weird thing about quantum mechanics as currently understood is that Born's rule seems to suggest that the binding of qualia is a separate rule in fundamental physics.