Don't forget about the labrys, it is also secreting the mixture of blood and ichor.
I think one of the tablets (17) mentions that this was not originally the case, and that only after the labrys was used on Tithonus did it secrete the black ichor, and later blood red after being used on Asterion.
The labrys that we find locked up might be secreting the blood of Asterion (or Asterions mortal blood mixed with Tithonus ichor) and as it dries it forms the ever expanding obsidian we find behind Hermes basin. It has to be going somewhere. It would also play into Asterion thinking of himself of himself poorly till further into the good route.