Who says the universe can't "know" all the ways? That's like saying momentum can't be conserved because the universe can't know all the ways that we could transform momentum into other forms of energy and back again.

Momentum comes from the interaction of forces, there's nothing that's "needed" to know. Two billiard balls colliding and a billiard ball colliding with a ball of mud conserves momentum (in a vacuum, in space, etc) the same because it all boils down to forces. F=dP/dt

That's very different from "regardless how you throw the dice it will always "know" what you did".

In other words, we invented some concepts (force, momentum, energy) that exhibit a symmetry under various transformations.

It's only "very different" in superdeterminism because that which is conserved doesn't yet have a widely accepted formulation that you've internalized the way you've internalized the other common concepts in physics.