Your example 2, "the correct theory of everything is the lexicographically least algorithm with K-complexity 3^^^^3", has the same problem as the "islam is true" example. K-complexity is uncomputable.

However, "the correct theory of everything is the lexicographically least algorithm in <some specific language such as lambda calculus> with length 3^^^^3" is computable - and the universal prior probability for it is low, but reasonable given the length of the sentence - it's not related to the magnitude of 3^^^^3.

Here at LessWrong, we're used to using "3^^^^3" as a way to point to a generic very big number, and certainly if you replaced "3^^^^3" with an explicit random number of similar magnitude, then the prior would be very low. But 3^^^^3 is different than most numbers of that size - it has a very short description.

If there was evidence suggesting that there was a very large constant somewhere in our physics, and someone showed that the last few digits of that constant matched the last few digits of 3^^^^3, then we would jump towards the hypothesis that in fact, the number is exactly 3^^^^3.