>I understand that's your opinion and of course you know mine.
No, I really don't quite understand what you believe or what points you are trying to make. "Modeling humans with computational processes" (your term) and doing "non-computable things" are wildly different things to consider.
You seem to constantly conflate the two. The only connection would be that were humans known to be essentially performing non-trivial tasks that drew on powers transcending computational processes, well, that would be something. (I'd say your examples all fall well short, and some just don't even make sense in that specific context.) Its really hard to even come up with meaningful examples of any performance task that is clearly in principle "non-computable". Violating complexity (factoring really fast, solving TSP really fast) I suppose would count.
Statements like "not hardy to come up with problems no computer can solve" also completely muddy the discussion. That might be interesting if it were impossible to come up with a problem that some human couldn't solve. But its not and so what?
Ramanujan certainly strikes me as Edgar Cayce of math, but what does it lead you to believe? Does the mysteriousness of it all make you believe that these "non-computational" processes must be at world? Evidently yes, but it seems a very illogical position to me. Why are we in this modern era not always walking around in profound amazement at the miracles of our own technology? I'd say its just the dulling caused by constant exposure. For people not so dulled, it might be just as easy to convince them that supernatural forces were necessarily involved.
I suspect Ramanujan had his own methods that unfortunately remained a trade secret. Riemann was similar. They may have had certain brain centers that developed in ways quite out along the long tail. But in general, highly developed and effective search techniques through vast spaces of possibilities will always appear miraculous if their workings are hidden. No "non-computable" powers are needed.
Which also leads to why you would bring up chess? Chess is showing that with continual development chess programs are now beating the very best humans - with more development I expect they will completely dominate (I'm being generous - many would say they completely dominate already. Statistically they certainly do - most PCs still in service can run a chess program that will beat most humans.)