The idea of metaprobability still isn't particularly satisfying to me as a game-level strategy choice. It might be useful as a description of something my brain already does, and thus give me more information about how my brain relates to or emulates an AI capable of perfect Bayesian inference. But in terms of picking optimal strategies, perfect Bayesian inference has no subroutine called CalcMetaProbability.

My first thought was that your approach elevates your brain's state above states of the world as symbols in the decision graph, and calls the difference "Meta." By Luke's analogy, information about the black box is unstable, but all that means is that the (yes, single) probability value we get when we query the Bayesian network is conditionally dependent on nodes with a high degree of expected future change (including many nodes referring to your brain). If you maintain discipline and keep yourself (and your future selves) as a part of the system, you can as perfectly calculate your current self's expected probability without "metaprobability." If you're looking to (losslessly or otherwise) optimize your brain to calculate probabilities, then "metaprobability" is a useful concept. But then we're no longer playing the game, we're designing minds.