The distribution of the experiment results, say correlation in a Bell test, should not matter (significantly) on the choice of seed. But the single electron being sent through the experiment still needs to "know" what the outcome of my PRNG is in order to "know" if it should be spin up or spin down this time.

But the measurement setting (PRNG outcome) can be arbitrarily removed from the seed value (by combining PRNGs in various ways). So that doesn't sound very convincing to me.