The thing that you're describing is a lot like finding the stationary distribution of a Markov chain. Not all Markov chains have stationary distributions and I can't tell whether this one would, though if it does have one it would be unique. It's an interesting idea.

I should also note that it is not necessary to do anything like this to preform induction over multiple theories. Instead, we can just require a program that outputs known theories in addition to the new theory. We can ask them to be output in any form, such as predictions or source code, since converting source code to predictions is O(1) in program size. Then, if the different theories have more in common, the program computing them all will be shorter than one that must seperately specify elements of very different theories. A slightly different implementation of the same general principle is Schmidhuber's Optimal Ordered Problem Solver.