Feel like a hack would have been to try to force dialogue into an extractable form that stored a state model relevant to the game, even additional hacks like asking the opposing player to restate their understanding of prior agreements; disclosure that I have no idea how the game Diplomacy works, so might be irrelevant.
Beyond that, no idea how Facebook manages its AI research, but quick Google confirms my memory that Meta/Facebook has done prior research on enabling AI memory capabilities related to recall, forgetting, etc.; which I mention just in case you were not aware.
I would think you could avoid much of this issue by creating a more sophisticated structured game model and use the language model only for converting between structured and unstructured data.