You could also sense that your location is privileged, because the observable universe is neatly centered at it, but science will prioritize Copernican principle over your senses.
>But you can't do both at the same time.
This doesn't match what you do. Tracing extracts mortal's-eye view from God's-eye view, so in God's-eye view you have both.
>depend on my suspension of disbelief and acting as if my branch of the multiverse is privileged
If your branch exists, it's sufficient for your day to day life, there's not much else to disbelieve. There's no need for it to be privileged. Do you worry that Earth isn't more privileged than Mars?
>But no one has done it, and I'm pretty sure it can't be done.
But quantum physics doesn't allow it. It's quantitative science where all observed phenomena are computable. If they aren't computable, then quantum physics doesn't predict them and thus diverges from observation. And Schrödinger equation is how predictions are made, collapse and measurement only act on what already exists before them and don't create anything new. So if Born rule is an observed phenomenon, it must be computable from Schrödinger equation. Also if Born rule holds with certainty, then it's a pure state, and observation won't do anything to it, so Born rule can't be created by observation.
>There's probably a Nobel prize waiting for the person who turns that intuition into a theorem.
This was argued by Max Tegmark https://arxiv.org/abs/gr-qc/9702052 I thought it's a famous diagram https://en.wikipedia.org/wiki/File:Spacetime_dimensionality....