How to handle degrees of success in roll under systems

I’m working on an RPG system that uses 2d6 roll under Skill for resolutions. On paper this system looks really good so far, but I have one major issue: Degrees of Success, especially when it comes to Contest (Skill vs Skill) resolutions.

Status Quo

Your character’s Attribute + Skill (e.g. Charisma + Persuasion) form a Target Number that’s between 2 and 12. You roll 2d6, sum them, and the sum has to be equal to or lower than the Target Number. Rolling a 1 has a special positive meaning, rolling a 6 has a special negative meaning. Additionally, 2 ones are always a success, 2 sixes are always a failure, regardless of Skill.

The problem

Imagine 2 parties contesting each other:

  • Character A has a Target Number of 5 (pretty bad), and character B has a Target Number of 10 (pretty good).
  • Character A rolls a 5 and succeeds. Character B and rolls a 6 and succeeds.
  • Character B has the better Degree of Success, as the margin between the player’s roll and the character’s Skill is bigger than for Character A.

If you say that lower is better, a character with Target Number 2 (very, very bad), who rolled a 2, will always have a better Degree of Success over a character with a Target Number 12 (very, very good), who rolled a 3.

Naive solution

My approach was to subtract the rolled number from the character’s Skill. You have a Target Number of 6 and rolled a 4? 6-4=2. You have a Target Number of 11 and rolled a 3? 11-3=8. It works, but I’m worried that this resolution will be too slow for actual play – we all know these sessions that last for hours and nobody is able to count straight anymore.

The best solution would allow a player to determine the Degree of Success/Failure in the same step to see if the character succeeded or not.

Other systems

Other systems that handle Degrees of Success for rolling under mechanics:

  • Call of Cthulhu: You have certain threesholds (half your skill, 1/5 your skill) at which you score an increased Degree of Success. – very coarse when you only have 2d6 instead of a 1d100 (but could work)
  • Unknown Armies: Basically like Black Jack–you roll under your Skill threshold, but as high as possible. Doubles (11, 22, 33) are criticals. – sadly doesn’t work, as ones and sixes have a special meaning. Flipping the meaning (6 is good, 1 is bad) also is iffy, as it’s flipping the understanding, that you have to roll under a threshold.
  • ???

What other systems or resolution systems are there, that tackle this problem?