The hypothesis that the mind is computable but is using heuristics, of various levels of sophistication, explains the data better and is more parsimonious than your hypothesis, because we already have reason to believe that the mind uses heuristics extensively.
Where you see uncomputable oracular insights, others see computable combinations of heuristics. If you introspect deeply enough while problem-solving, you may be able to sense the heuristics working prior to the flash of intuition.