I may be repeating what Vladimir said here, but it seems to me your objection is basically "Oh shit! We can diagonalize!" (Which if we then collapse the levels can get us a Berry paradox, and others...)

So, yes, it follows that any system of description we can think of, there's some potential truth its corresponding "universal prior" (question - do those exist in general?) won't be able to infer. But the fact that this applies to any such system means we can't use it as a criterion to decide between them. At some point we have to just stop and say, "No, you are not allowed to refer to this concept in formulating descriptions." Maybe computability isn't the best one, but you don't seem to have actually given evidence that would support any other such system over it.

Or am I just missing something big here?