I apologize if this has been talked about or proposed before (I assume it has, but don't recall it).
I think the Turn Undead Table in Labyrinth Lord (or any early version of DnD or it's retroclones) would make an excellent skeleton for Skill Resolution.
Assuming we used Backgrounds and not Non-Weapon Proficiencies:
A Background has the chance to either permit an automatic success or increase your level by 1.
If an appropriate Ability Score is 12 or better, increase your level 1.
Then find your level + modifiers, cross reference by the Threat Level of the Task and look for auto success, a target number on a d20 or automatic failure.
Pretty straightforward if you ask me.
Thieves would get to first roll their Thief Skill Percentage, if they fail they may still try to roll on the Skill Resolution Table. Essentially, Thief Skills can be thought of as an extra chance at success or a chance to critically succeed.