Didn't the Architect theorize that certain groups of Humans/Elves/Qunari/etc. could have a natural resistance to the taint, and that infecting most of the population with the taint would single out those immune(like Fiona, and arguably Alistair)?
Both in game and in the supplementary novels, I've always got the impression The Taint functioned like an infection, a sickness, like rabies, a virus, a fungus or something.
Even people who might not be totally immune, like Lelianna, have been shown to be incredibly resistant to The Taint's corruption, which again implies the immune system plays some role in fighting it off.
Perhaps some combination of blood magic and dragon's blood could (even temporarily) cleanse the body of the taint.
Here's a thought: The Darkspawn, including Corypheus/The Architect, arguably existed in the taint-infested Deep Roads for hundreds of years----so what if the taint itself induced some form of immortality (or at least halting the aging process), but inducing early onset dementia/Alzheimer's?
If Avernus's used Blood Magic to cleanse himself of the negative aspects of The Taint from time to time, it would explain his impossible age, and how we was able to cheat the calling.
Furthermore, assuming Arlathan is The Black City, where Elves enjoyed immortality(or near immortality), then perhaps they were all infused with The Taint, and used some similar cleansing ritual to avoid it's negative effects, like the mental degradation and The Calling. If that was the case, then when the Ancient Elven and Arlathan[The Black City] was eventually banished to The Fade, it was already infested with The Taint/The Corruption. Furthermore, since Corypheus states that not only has the taint existed in Thedas before the first blight, but that The Black City was ruined/empty/tainted upon The Magisters' arrival.
But that still doesn't explain why Arlathan was banished to begin with. Perhaps it was a kindness. If The Calling is truly some psychic-subliminal messaging from The Old Gods, then perhaps Solas banished his Civilization to The Fade as attempt to save his people from the madness that was The Old Gods call. After all, what better place to escape the call of The Old Gods than another dimension?
That still doesn't explain what The Taint is or how The Old Gods are binded to the Corruption/Tainted ones, but it would at least give some insight on how one could possible avoid it's negative effects (aka: blood magic).