Probability is a state of your knowledge.

Two things to say:

1. You're ruling out the possibility that the laws of physics are objectively probabilistic. (If they can be 'objectively quantum' why not 'objectively probabilistic'?)
2. Even if you dogmatically insist that this is impossible in principle, we could still imagine a variation of my 'Theory 2' where the coin events are determined by the values of an algorithmically random sequence. The algorithmic randomness would be a property of the sequence itself, not anyone's knowledge of it.

Quantum superposition has nothing to do with how much you know.

Quantum superposition has "quite a lot" to do with the Born probabilities, and (according to you) the Born probabilities, being mere probabilities, have everything to do with how much you know.

I'm not saying a quantum universe is a probabilistic one. But that's really the whole point - it's neither probabilistic nor deterministic (except in the same vacuous sense that you can make it look deterministic if you carry the entire distribution around with you).