Also, since the scenario said we've done this many times and we haven't been trolleyed yet, it can't be all that easy to get trolleyed.

Maybe you get run over by the trolley only if you try to factor Omega's number, and all the times before this Omega's number and the lottery number were different, and there's no much point in trying to factor the lottery number in that case since (assuming linear utility of money) it has no relevance on how many boxes you should take.