I've lurked here for a while. As you can see I registered to respond to this post. Anyway, it seems like you have some interesting ideas. My questions are what exactly are you trying to do? When you talk about deriving the values of any given situation from the model, it seems like what you'll want is some kind of game theoretic solution that gives you the optimal course of action for any given situation and then the expected value for the optimal action, but I want to make sure I understand what you're trying to do.

If this is what you're trying to do, then I think you want to do this in a game theory framework. Look for perfect Bayesian equilibria and then (since you'll never be on the equilibrium path) try to use the same logic to figure out what happens off the equilibrium path, and then calculate the expected outcomes of those.

From what you've done so far, I have the following thoughts:
1. 32 axioms is an awful lot. Too many axioms is usually a sign of a bad model. Sacrifice some accuracy for simplicity and clarity. A model that is a bit inaccurate is better than one that is more accurate but too complicated to solve.
2. Use the standard game theory technique. Work out optimal play at the river given any possible beliefs about what your opponents hold. This is difficult, but not THAT difficult relative to the problem. Once you have that, start working out the value of reaching the river in any given situation. After that, start thinking about turn play given what we know about the river. Then you'll have some basis for starting to think about how people form their beliefs on the river. Eventually, you'll start to figure out the relationship between turn play and river beliefs and using the combination of the ability for turn play to influence river beliefs and the river outcomes given beliefs you'll have a model of turn and river play. Now we repeat this process and get back all the way to preflop.

This really is a pretty difficult problem. My other suggestion is to start with limit play because the information is more limited which makes belief formation a lot easier to model. The problem with NL is that bets are essentially continuous which means you'll probably need fairly complicated functions to explain belief formations (or you can reduce the way we look at bets to discrete values (ie underbet, overbet, etc) but then you sacrifice some clarity since where we put the borders are arbitrary). I hope this is some help, if you work further on this I'd be interested in seeing how it develops.