I found it interesting that Asterion was taken despite the votes in his trial being in his favour. Hades himself said that Asterion had already died, and been judged in Hades, and that the trial was a farce with no jurisdiction over the underworld. Asterion is feared by many of the gods due to his mastery over the Threadcutter, a labrys enchanted by Zeus' ichorous blood (the black stuff dripping from the axe head in the basement), which can kill immortal beings.
I think the Threadcutter will be a central plot point, as Asterion was mentioned to have mastered it, which makes the gods afraid. Interestingly, it might be one of Asterion's only ways out too, since he, himself, is an immortal being. However since it burns any mortal who touches it, Asterion might once more need to die in a rather 'unworthy' way.
As for a happy ending, that's actually something I'm writing currently, a fan fiction. It takes place in Asphodel, Asterion and MC sitting side by side at the river Lethe, weaving flower crowns for each other, having a soft argument about drinking from the river. But it would also mean forgetting his friends and the joys he had in life, as well as his suffering.