Also, if these super-Turing machines are possible, and the real universe is finite, then we are living in a simulation with probability 1, because you could use them to simulate infinitely many observer-seconds.

This is probably true. I think a lot of people feel uncomfortable with the possibility of us living in a simulation, because we'd be in a "less real" universe or we'd be under the complete control of the simulators, or various other complaints. But if such super-Turing machines are possible, then the simulated nature of the universe wouldn't really matter. Unless the simulators intervened to prevent it, we could "escape" by running an infinite simulation of ourselves. It would almost be like entering an ontologically separate reality.