Just to put it out, I’m absolutely loving this discussion😛
But on one of the points you raised
“All sciences must work with tolerances to some specified resolution, be it in measurement or statistical.”
I don’t think this is true either, if a theory is in fact true it should be able to predict occurrences to the utmost amount of scrutiny possible and it should do so reproducibly.
If it fails to do so there is something wrong with it.
If you mean resolution of the measurement devices, then that’s a limitation on the device not the science or theory if the theory is true it must be true for when we have better devices.