Suppose we define a generalized version of Solomonoff Induction based on some second-order logic. The truth predicate for this logic can’t be defined within the logic and therefore a device that can decide the truth value of arbitrary statements in this logical has no finite description within this logic. If an alien claimed to have such a device, this generalized Solomonoff induction would assign the hypothesis that they're telling the truth zero probability, whereas we would assign it some small but positive probability.

I'm not sure I understand you correctly, but there are two immediate problems with this:

• If the goal is to figure out how useful Solomonoff induction is, then "a generalized version of Solomonoff Induction based on some second-order logic" is not relevant. We don't need random generalizations of Solomonoff induction to work in order to decide whether Solomonoff induction works. I think this is repairable, see below.
• Whether the alien has a device that does such-and-such is not a property of the world, so Solomonoff induction does not assign a probability to it. At any given time, all you have observed is the behavior of the device for some finite past, and perhaps what the inside of the device looks like, if you get to see. Any finite amount of past observations will be assigned positive probability by the universal prior so there is never a moment when you encounter a contradiction.

If I understand your issue right, you can explore the same issue using stock Solomonoff induction: What happens if an alien shows up with a device that produces some uncomputable result? The prior probability of the present situation will become progressively smaller as you make more observations and asymptotically approach zero. If we assume quantum mechanics really is nondeterministic, that will be the normal case anyway, so nothing special is happening here.