Ironically, I see this the other way around. I think people are having a hard time accepting the possibility that humans are partial halting oracles because of their bias against anything that seems religious, even if it makes more sense.
If you're interested in Bayesian approximations of mutual information check out the references listed at [1] and tell me what you think, as this is far from my speciality.
[1]https://en.m.wikipedia.org/wiki/Mutual_information#Bayesian_...
I evaluate this issue with a Bayesian + max entropy approach. We have two hypotheses:
1. humans are TMs
2. humans are PHOs
Max entropy weights these hypotheses equally. What humans do is given the highest expectation with #2. Thus, Bayesian hypothesis selection says #2 is the most likely explanation of the evidence. Inference to the best explanation says humans are PHOs.
I have a similar approach to gravity. There are two hypotheses
1. The gravitational field comes about from the curvature of spacetime
2. The ghost of Einstein flies around through all of space at an impossibly high speed nudging all objects such that their trajectories align with what he would find elegant.
Max entropy weights these hypotheses equally. What h̶u̶m̶a̶n̶s̶ planets do is given the highest expectation with #2. Thus, Bayesian hypothesis selection says #2 is the most likely explanation of the evidence. Inference to the best explanation says h̶u̶m̶a̶n̶s̶ ̶a̶r̶e̶ ̶P̶H̶O̶s̶ gravity is Einstein's ghost.
I have a hard time seeing your argument as anything other than 'motivated reasoning' attempting to justify to your religious/metaphysical beliefs.