This immediately made me think of the "hazard" bit in the D&D5 doc. Basically, if you fail by 10 or more your REALLY blow it. It might be nice to think of it that way. If the roll is close, then you can roll again or burn luck, if its not even close, then you messed it up. In the event of a re-roll, I'd definitely make wandering encounter checks, as appropriate.
As for your backstab rule, I am totally into Warrior Deeds allowing Backstabs, but I probably wouldn't ask for a further Stealth check. I do like the idea of higher Deed rolls offering higher bonuses. Maybe Deed based backstabs could be limited ones that are auto crits for thieves, but with bonuses to hit = (Deed roll -2).
The problem with failure thresholds (fail by 10 or more) is that (1) there is more math involved, and (2) it doesn't remove the ON/OFF switch. If the player has a bonus of +5, and the DC is 15 or less, the switch is ON, because the player can always roll closer than 10. Meanwhile, the DC must be set to 36+ before the character both fails and knows he cannot potentially succeed (without burning Luck). Again, characters are encouraged to just keep rolling (if they can), and the Judge is encouraged to decide ahead of time whether or not he wants this particular lock to be picked (i.e., should he set the switch to ON or OFF?). More fun, IMHO, to design adventures where the dice determine outcome, and both Judge and players must be prepared for some lateral thinking.
EDIT: Oh, and that "hazard" bit is from 3.0 before it showed up again in 5e's materials. In 3e, you can suffer different penalties from a failure of 5 or more or a failure of 10 or more.
As for the Backstab rule, consider the following:
(1) You would probably not allow a Warrior to use a Deed to gain an automatic Critical.
(2) The discussion of Deeds explicitly allows for saves or other checks to be required for the Deed result to occur.
(3) You don't want the Warrior to simply become the set-up guy for the Thief in every combat, or change the Thief's forte from "stealthy guy" to "guy who stabs people after the Warrior distracts them". You don't want this to be the One Obvious Deed that gets used all the time because it is obviously so much better than everything else. A good option? Yes. The obviously optimal option in most circumstances? No. Otherwise the Warrior becomes the Thief's stooge, and the Thief becomes the mighty melee opponent who actually drops most of the foes.