Don't the physical facts underdetermine what computation ('abstracted idealized dynamic') my brain might be interpreted as performing?

I would think they do in the same sense that the physical facts always underdetermine the computations that the universe is actually performing. That's obviously a problem with trying to implement anything - though how much of a problem depends on how robust your implementation is to having the wrong model: bridges still stand, even though we don't have a perfect model of the universe. But it doesn't strike me as a problem with the theory per se

(I'm not sure whether you were suggesting it was.)