Usually when there's a paradox like this, it means we've chosen bad axioms somewhere. Even things that seem intuitively self-evident can prove untrue.

For example, what if time does not necessarily flow in a single direction at the quantum scale; what if instead, the ground level of physical reality is a timeless information graph / equation that is 'solved by the universe'?

I'm no physicist and no nearly nothing about the real math of QM, but every time I read these lay-explanations of "quantum weirdness" and "wave function collapse", I get this strange feeling that we're thinking about time all wrong: What if unidirectional time is an illusion? What if causality (and inference) is an illusion (thus explaining how hard it is to capture it mathematically)?