“you were suggesting that some form of mystic insight may enable a being to transcend this seemingly unresovable paradox.”

This is exactly my point and the main reason I hurried to dismiss the idea that I held rigidly to a scientific view.

Modern scientists do not incorporate the views of ancient and even simple people today who can see different states and can perceive the working of nature on simultaneous levels.
So many concepts can be different if interpreted through a different state.

“I see what you are saying in principle, but the practicalities of, for example, measuring a particles behavior in both space and time would require not just a unique state of consciousness, but also some pretty sophisticated equipment to go along with it.”

I smile :)
Might I suggest that another developed brain is the ideal sophisticated equipment for measuring past present and future (time and space)?

One View can be superimposed on another and the person with insight can see no contradictions in what appears to be contradictory positions while other people could be thoroughly confused.

Many indigenous people had many ‘gods’ while proclaiming one ‘god’ and to them there was no contradiction in what appeared to others as contradictions. Many were labeled heathens, pagans and many were killed because of these apparent contradictions. They were simply viewing the world differently. Modern scientists (not all but most) dismiss such cultural vision. But these “contradictions” can be reasonably explained and understood.