Thus, what the AIXI will do is this: it will move right, then it will do nothing for the rest of time. But while the AIXI is simulating the Turing machine that rewrites itself into a stupid machine, the AIXI itself has not eliminated the AIXI code.

I don't think it would do even this. (A computable approximation of) AIXI thinks it only affects the universe through its output signals. Since there is no output signal that would cause AIXI (regarded this time as an element in its own universe model) to be reprogrammed, the solution would be completely inaccessible to it.