In this setup, the AIXI is motivated to increase the number of Grues in its universe (its utility is the time integral of the number of Grues at each time-step, with some cutoff or discounting).

AIXI has a sensory reward channel. It maximizes the sum of the future sensory reward channel. It can't be rewarded by a number of Grues. You could try to send info down the reward channel based on the number of Grues, but AIXI would rip the controls out of your hands if possible. AIXI lives in a world of integer sequences. To it, no such things as Grues can ever be considered, except insofar as they are hidden variables in an opaque predictor which generates an integer sequence. Nothing else, like time-skipping, matters to AIXI except insofar as an integer sequence changes. I am unable to understand or verify your logic here, since you're not explaining what happens to integer sequences being predicted by Solomonoff induction.