a few things. the end you get isn't based of how any times you send asterion out. there's 2 choices in the ruthless route
so for example, in the choice of 2 options, one gives you endings A, B or C, depending on what you choose on the three options choice, and the other gives you ending D regardless of what you choose the triple choice.
the elixir isn't poison, it's ichor, the blood of immortals. it's toxic for humans, but harmless to gods.
and lastly, what makes you think hermes could do anything? the gods don't have free will the same way we do, plus they are bound by magic to not interfere in the hotel. else we'd be having open war right there. trust that greek gods do not care for familial bonds that much, they beef all the time.