Omega (who experience has shown is always truthful) presents the usual two boxes A and B and announces the following. "Before you entered the room, I ran a simulation of this problem as presented to an agent running TDT.

If he's always truthful, then he didn't lie to the simulation either and this means that he did infinitely many simulations before that. So assume he says "Either before you entered the room I ran a simulation of this problem as presented to an agent running TDT, or you are such a simulation yourself and I'm going to present this problem to the real you afterwards", or something similar. If he says different things to you and to your simulation instead, then it's not obvious you'll give the same answer.

Are these really "fair" problems? Is there some intelligible sense in which they are not fair, but Newcomb's problem is fair?

Well, a TDT agent has indexical uncertainty about whether or not they're in the simulation, whereas a CDT or EDT agent doesn't. But I haven't thought this through yet, so it might turn out to be irrelevant.