Hmmm, maybe the answer to this one lies in the middle of that list? Asterion is the one smelling you and he finds saltwater (but no sunlight, leftover from our interaction and blessing from Poseidon?), crocus (makes saffron), and 'decaying petals of deflowered poppies'. THEN gets the smell of the pungent oil and the coppery taste, and finally your human smell. I'm not sure why we smell like crocus and poppies, but of note are the histories/ties of those two flowers:
- Crocus has two mentioned myths on wikipedia, the more relevant one is this: he was a companion to Hermes that was accidentally killed by said god in a discus accident, and in his grief, he turned his corpse into the crocus flower. (Of note, this is a very similar myth to Apollo and Hyacinth, but Apollo hasn't been very central to anything yet). - Maybe this is Hermes' 'scent' and our brushes with him has it lingering on us? Dangit I feel like I need to playthrough yet again and focus on every smell that gets mentioned, lol.
- Poppies are heavily associated with sleep and death, said to be created by Demeter so she could get some damn shut eye. They're common offerings to the dead, so their scent might make Asterion think of death and even specifically his death. (They're also heavily associated with Hypnos, god of sleep, and Morpheus, god of dreams, but neither of those two have been mentioned in the novel, so I think we can rule them out for now)
So, I think the smell of poppies makes him think back to his death, leading to the oil smell and coppery taste. You're right about Charon's payment, but since we know it was a gold coin and that gold doesn't taste coppery, I think it was just the blood welling 'up' from the wound as Asterion lay dying - final moments and whatnot. The bitter, burnt oil smell may be from the profaned shrine there in the labyrinth, then? It seems like a dark, cloying scent that might be used to describe defilement, which we know the shrine had been.
Wait hang on, this is right about when the achievement called 'The Tale of Asterion and Theseus' fires, right? With its' description of "Rewrite the story of Asterion and his executioner"... I think we just accidentally did a biiiiiiiiiig recursion breaking ritual where we took Asterion's story and changed it: Man chases minotaur through a labyrinth (literally what just happened in the Deep Labyrinth), man catches minotaur, they fight (note the fight's beginning is when Asterion's birthmark 'first' appears), man someone wins (huh, turns out Asterion can win if you try to double down on strength, like a fool)... but then the man never slays the hybrid (well, until later chapters when we take him to bed, wink). Asterion's story is supposed to have him decapitated, so the ring of fire starts closing in on his neck, but the MC's gentle touch breaks the recursion and rewrite's Asterion's story.
He had been seen as a coward for letting himself be killed without a fight, but this time he does fight (playfully though it was) and that's right when his birthmark reappears. Even though they argued to the judges that it was not a shameful act but instead a holy sacrifice to the gods, now it's not even a shameful act: he fought, we won, and we did not kill Asterion. One of the reasons the gods shoved Asterion in this realm might've just been erased by our actions, hence all the weirdness.
EDIT: Just adding some extra evidence, when you catch Asterion in the deep labyrinth chase and hug, he "lets out a grunt - liberating, redeeming, as though a lock had come undone in his throat."
EDIT 2, THE REVENGE: Oh and the god that gave the Roman coin that translates things? Very likely Hermes, which can also explain the smell of crocus in the area since that was one of the offerings to the fire when updating the translation magic. AND that's not even highlighting the actual ritual that occurred down there: a fire, a sacrifice, a story (the hotel's origins), unveiled truths (why Asterion will still call you Master and King); all things Oscar teaches us when he's narrating his ritual for Pedro. Sure they were intended for the translation magic, but that might not stop them from mattering here, we 100% just did some sort of accidental ritual, likely to restoke Asterion's divinity that, as Robert said, had been bled dry from him.