The part about the reasoners having an arbitrary amount of time to think wasn't obvious to me. The TM can run for arbitrarily long but if it is simulating a universe and using the universe to determine its output then the TM needs to specify a system for reading from the universe.
If that system involves a start-to-read time that is long enough for the in-universe life to reason about the universal prior then that time specification alone would take a huge number of bits.
On the other hand, I could imagine a scheme that looks for a specific short trigger sequence at a particular spatial location then starts reading out. If this trigger sequence is unlikely to occur naturally then the civilization would have as long as they want to reason about the prior. So overall it does seem plausible to me now to allow for arbitrarily long in-universe time.