If I took the scenario at face value -- in other words, treating the question as one of pure mathematics -- the mathematical answer is of course BusyBeaver(me).

I presume that (me) is supposed to be some large number here. This leads to a separate question- is Omega limited to Turing computable calculations? It isn't normally relevant to what Omega can do, but I'll be slightly annoyed if I say to Omega BusyBeaver(1000) and Omega gets embarrassed for having limits.