Ultimately I think you’ll encounter a difficulty here due to epistemic circularity: you’ll eventually need to know about a distribution you can’t go more meta on because it would be functionally equivalent to solving the problem of the criterion, discovering completely the universal prior, grounding induction in general, etc.. Not that we don’t always have to deal with it, just that in particular I don’t expect going meta to help much beyond reducing the number of free variables you have to consider. That being said, getting the number of free variables you have to think about down is helpful, but you’ll still be left with them.

Ultimately I think you’ll encounter a difficulty here due to epistemic circularity: you’ll eventually need to know about a distribution you can’t go more meta on because it would be functionally equivalent to solving the problem of the criterion, discovering completely the universal prior, grounding induction in general, etc.. Not that we don’t always have to deal with it, just that in particular I don’t expect going meta to help much beyond reducing the number of free variables you have to consider. That being said, getting the number of free variables you have to think about down is helpful, but you’ll still be left with them.