Well, maybe I'm not understanding you perfectly here, Nebullis; but it seems to me the "proof" to be had in your children has nothing to do with the "mechanical." I have to maintain that position, until such time as "mechanical" considerations and operations can be shown -- unilaterally -- to produce the life of your offspring; which I imagine you had a little "closer-in" help to get (or "beget") in the first place. (That should be fun!)
Without that "closer-in help," your beautiful kids would not have been born.
A Theory of Everything will not give us a working model for investing in the stock market.
It seems to me that, to the extent that successful investing in the stock market is dependent in some way on public perceptions -- that is, on "mass perceptions and feelings" -- then there will unavoidably be an element of chance involved. But IMO this is a different "scale" of the problem we've been discussing. To say as much does not necessarily impugn -- it seems to me -- the fundamental order of the Universe, which does not appear to be ruled by pure chance in its main outline (so to speak).
But I do agree with you: Conceivably, a "theory of Everything" would have to take this sort of thing (e.g., stock market behavior) into account. Which is to say: It must account for what is susceptible to random changes, as well as what is not subject to random changes. JMHO FWIW.
I went back and did some refresher reading on algorithmic Theories of Everything - and as you and Nebullis imply, strong determinism is the unavoidable conclusion of naturalist TOEs, i.e. predestination wins in a shutout.
Like in the "consciousness is the physical phenomenon of the brain" hypothesis, as free will goes so does personal accountability, morals/justice, philosophy, theology, etc.
IMHO, despite all attempts of science to stay out of the metaphysical, these areas of research will always stir the "predestination v free will" pot.