perhaps some astrophysical observation of yours that isn't available to the AI

The best approach I know now for constructing an FAI is CEV. An AI that can pull that off should be able to also access any astrophysical data I possess. I am not sure what the point would be if it didn't. The expected utility of programming the FAI to be able to figure this stuff out is much higher than building it a giant lookup table of stuff I know, unless I had magical advance knowledge that some particular fact that I know will be incredibly useful to the FAI.

My intent was to use a digit large enough that the AI cannot compute it in the time Omega is allowing it; I don't see any difference between your version and mine, then?

Yes, there is no difference, given that you have a sufficiently large digit. The reason I brought up my version is so that you don't have to worry about computing the truth value of the logical proposition as a strategy, as you don't even know which logical proposition was used.