The creation of the Wardens is something I did as a Fanfic, exploring some possibilities with words. What I came up with was that it was the Tevinter version of Project: Rebirth; the idea to creating a super soldier. What I had were the failures; mixing of different ingredients and ideas to create a sort of Captain Tevinter that would fight a War against Dumat (I didn't call it the Blight because it was the first and only one in their mind) since it had been going on for soething like 150 years at that time. One of the thoughts I had was that they eventually recognized that killing Dumat wasn't sufficing (they had done it multiple times, and it took them a few times to realize that it was the same being instead of another one rising up when the first died).
How desperate they must have been, fighting against the very end of the world... and losing.
The Grey Warden Formula (what I called it) was the result of dozens, if not hundreds, of faulty experiments, to include how much Lyrium, Darkspawn Blood, and Archdemon blood to us (like any other chemical equation). There had to been failures (those poor volunteers and slaves!) and they probably tripped over a better one but because it killed the first few people, it got shelved.
The very first warden, I made an Elvish Slave (because you know that it makes sense). While the non-Warden Tevinters dismissed this survivor and banished him to whatever shithole life he had, subsequent Wardens could always feel him, their ultimate progenitor. Despite that the rest were Human Tevinters (warriors and mages), they couldn't get the 'feeling' of the very first of their kind. Which is why they insisted that he join, be trained and armed and allowed to fight.
That's how I got to the point where Wardens accepted 'anyone''; some of the experiments were slaves, elves, prisoners, political opponents... and they began surviving as well as the intentional warriors and mages. With such a group together, 'feeling' one another through the Taint... they bonded.
That's how I see the birth of the Grey Wardens.