I think you are conflating these things. I agree that Poseidon was the person who sent the deed. However, I believe it is Zeus who is the person we see in the prologue, given Hermes mentioning that his father was basically losing his mind and both of them being described as jittery with coffee.
Viewing post in [Spoilers]The true identity of the old man
not necessarily, i also got the impression they were implying zeus since hermes was refering to him as old man, which is a common way someone may refer to their father. also, if you read the trial logs, you can see that zeus wasn't particulary eager to vote one way or the other but, with the pressure of bringing the trial to an end, he likely rushed his vote. there's the possibility that he came to regret his vote later and, extrapolating a bit, the results of the trial might have led to the downfall of the olympians. naturally this is all conjecture with no confirmation whatsoever, but it could work with the narrative available to us. the one thing that doesn't fit is that the letter was signed P.
Zeus was actually in Asterion's favor? I have only collected Hera's voting letter and it said Zeus was against the bull(I mean I have collected almost all of the voting letters, but still missing Zeus', Athena's and Apollo's). I've only done 3 reruns of the game and skipped through the Hinterlands' plot to save some time and focus on collecting informations from the main events at the hotel.