You are applying a decision theory to the node C, which means you are implicitly stating: there are multiple possible choices to be made at this point, and this decision can be made independent of nodes not in front of this one. This means that your model does not model the Newcomb's problem we have been discussing - it models another problem, where C can have values independent of P, which is indeed solved by two-boxing.

It is not the decision theory's responsibility to know that the values of node C is somehow supposed to retrospectively alter the state of the branch the decision theory is working in. This is, however,a consequence of the modelling you do. You are on purpose applying CDT too late in your network, such that P and thus the cost of being a two-boxer has gone over the horizon and such that the node C must affect P backwards, not because the problem actually contains backwards causality, but because you want to fix the value of nodes in the wrong order.

If you do not want to make the assumption of free choice at C, then you can just not promote it to an action node. If the decision at C is casually determined from A, then you can apply a decision theory at node A and follow the causal inference. Then you will, once again, get a correct answer from CDT, this time for the version of Newcomb's problem where A and C are fully correlated.

If you refuse to reevaluate your model, then we might as well leave it at this. I do agree that if you insist on applying CDT at C in your model, then it will two-box. I do not agree that this is a problem.