whether the universe somehow allows someone within the universe to precisely simulate the future faster than it actually comes - a proposition I don't believe is ever true in any universe defined mathematically

As near as I can tell, this depends on dubious assumptions about a mathematical universe. You appear to treat time as fundamental, and yet reject the possibility that reality (or the Matrix) simulates a certain outcome happening at a certain time, not before (as we'd expect if reality calculated the output of a time-dependent wavefunction).

In addition, you seem to assume that reality cares about the same aspects of the situation that interest Omega. Otherwise it seems clear that Omega could get an answer sooner by leaving out all the details which don't affect the human-level outcome.