If the mind were found to be uncomputable, I think you'd find vastly more physicists would take that as evidence the universe is uncomputable than that the mind is nonphysical.

So they may, but that would not follow logically. If the lowest level of physics is all computable then the higher physical levels must also be computable. Thus, if a higher level is not computable, it is not physical. We have never found anything at the lowest level that is not computable. None of it is even at the level of a Turing machine, unlike human produced computers.

Any chaotic system (highly sensitive to initial conditions) is practically uncomputable for us, because we have neither the computational power nor the ability to measure the initial conditions sufficiently accurately. Whether there is some lowest level at which everything is quantized, or it's real numbers all the way down, is an open question.

I don't think your argument will seem compelling to anyone who doesn't already have a strong prior belief that the mind is non-physical.

I would argue it is the other way around. If people are truly unbiased whether we are computable or not, then they would give my argument consideration. It is those with a priori computational bias that will not be phased by what I say.

You're right, but people tend to have strong priors one way of the other, often unconsciously. This is one of those classic cases where people with strong, divergent priors will disagree more strongly after seeing the same evidence. So if you want to convince people you'll have to try harder than most to find common ground.

And that's why I'm not concerned with convincing anyone. The proof is in the pudding. If I'm right, I should be able to get results. If not, then my argument doesn't matter.