If a counterfactual version of A is told outright that O(A)==1, and yet sees a provable way to make O(A)==2, how do you justify not going crazy?
It's not the correct way of interpreting observations, you shouldn't let observations drive you crazy. Here, we have A's action-definition that is given in factorized form: action=A(O("A")). Normally, you'd treat such decompositions as explicit dependence bias, and try substituting everything in before starting to reason about what would happen if. But if O("A") is an observation, then you're not deciding action, that is A(O("A")). Instead, you're deciding just A(-), an Observations -> Actions map. So being told that you've observed "no award" doesn't mean that you now know that O("A")="no award". It just means that you're the subagent responsible for deciding a response to parameter "no award" in the strategy for A(-). You might also want to acausally coordinate with the subagent that is deciding the other part of that same strategy, a response to "award".
And this all holds even if the agent knows what O("A") means, it would just be a bad idea to not include O("A") as part of the agent in that case, and so optimize the overall A(O("A")) instead of the smaller A(-).
At this point it seems we're arguing over how to better formalize the original problem. The post asked what you should reply to Omega. Your reformulation asks what counterfactual-you should reply to counterfactual-Omega that doesn't even have to say the same thing as the original Omega, and whose judgment of you came from the counterfactual void rather than from looking at you. I'm not sure this constitutes a fair translation. Some of the commenters here (e.g. prase) seem to intuitively lean toward my interpretation - I agree it's not UDT-like, but think it might turn out useful.
This problem is roughly isomorphic to the branch of Transparent Newcomb (version 1, version 2) where box B is empty, but it's simpler.
Here's a diagram: