Depends, if the crime is murder how do you count the harm caused by ending someone's near-infinite life?

The retributive aspect of punishment doesn't attempt to compensate directly for harm to the victim; it attempts to give the people affected by the crime fuzzies by doing bad things to the perpetrator. The victim or victims can't be accounted for in this dimension of the problem; they're dead and cannot receive fuzzies. Hence the qualification.

I haven't fully worked out my theory of deterrence, but the crude first approximation, as briefly discussed here, is that the disutility to the criminal of the punishment should be greater than the utility they received from committing the crime, adjusted for things like probability of getting caught.

That sounds reasonable, and I think it's consistent with my model.

I don't think that your typical prison inmate is a perfect Bayesian.

I rather think that that should be, ideally, adjusted so that overall utility is maximized (weighing the utility of prisoners equally as the utility of the rest), which will be vastly different both from reality and from your model assuming the above proposition.