Most dungeon achievement characters were previously available in limited-time events, with the dungeon serving as a permanant way to acquire them. Templar Crusader might be the first one that was part of a month-long mega-event though? It's certainly the first of these characters that I've owned myself before the dungeon launched.
Oh wow, swapping out the Envious on my Templar (I mistakenly mixed up Crusader and Templar in my original post) and replacing them with Lanterns has easily shaved at least 20s off my average times. Tears through that first stage too. It's the interaction between Lantern's healing and Templar's damage when healed passive right?