Is the trick with problem 1 that what you are really doing, by using a simulation, is having an agent use timeless decision theory in a context where they can't use timeless decision theory? The simulated agent doesn't know about the external agent. Or, you could say, it's impossible for it to be timeless; the directionality of time (simulation first, external agent moves second) is enforced in a way that makes it impossible for the simulated agent to reason across that time barrier. Therefore it's not fair to call what it decides "timeless decision theory".