I went back and reread the labyrinth constitution, you're correct, I must have misremembered reading that the order of succession ended with Zeus and not the Overseer so it would make sense for Hermes to have been the Old Man at the start. Hermes makes the most sense for being the Overseer since just based on his Greek lore and the fact that since the only Olympian to be allowed to enter the realm is the one voted as Overseer. Nikos will mention that he answers to him if you uncover Argos' true identity after the Hermes nearly killed him and Pedro. I do wonder what was Herme's intention with the letter and what his logic behind that subterfuge was; even if it doesn't make an actual logical sense or is just born out of the madness overtaking him.
Step 1: Pretend nonsensical letter he delivered was written by the old man that gave the deed to the MC, who he believes is Clement. Despite the fact that he first said that he didn't remember who sent the letter in the first place despite being the same name as his fake last name. Causing Asterion untold distress.
Step 2: ???
Step 3: Profit. Minotaur Make-out Motel established.
It could also be as simple as he wanted to fuck with them because he is a trickster.
I haven't had a chance to see the other Ruthless endings but I have read the While You Live ending. If it uses the Old Man sprite in the ending to represent the MC, I see that just being poetic of the theme of recursion and not meant as a definite identity of the Old Man that gave the deed at the start.