This seems to be the observation that you can't have a Turing machine that implements AIXI. An approximate AIXI is not going to be able to simulate itself.

Yes, I guess you're right. But doesn't this also mean that no computable approximation of AIXI will ever hypothesize a world that contains a model of itself, for if it did then it will go into the infinite loop I described. So it seems the problem of Model 2 will never come up?

The main issue is that before you get to leverage the first N bits of AIXI's output you have to also explain the first N bits of AIXI's input

Not sure I'm understanding you correctly but this seems wrong. AIXI conditions on all its outputs so far, right? So if the world is a bit-repeater then one valid model of the world is literally a bit repeater, which explains the inputs but not the outputs.