Make higher rolls better, assign absolute thresholds for levels of success

This was a solution used by (among others I’m sure) Fading Suns. In their Victory Point system, a player rolled a d20, trying to roll as high as possible while still rolling under the total of their applicable attribute plus applicable skill plus/minus any difficulty modifiers. The higher the roll, the more “victory points” awarded (per a little table on the character sheet), and getting more than an opponent matters. If you roll exactly the target, that’s a critical success, doubling your victory points; a 1 always succeeds, a 19 always fails, and a 20 is a critical fail (which spoils the otherwise elegant basic idea of “higher is better, up to the limit of your ability”, but still...)

A simpler version of this could work in your case, adjusting for the 2d6’s different probability curve (results in the middle of the range are significantly more likely). But it has the benefit of modelling that someone who is more skilled has a definite edge, as they are not only more likely to succeed but to succeed better.

Another example would be the Resistance Engine used in Spire and Heart; while the basic mechanic is very different (skill equivalents grant you extra dice to roll, and you use your highest single result), the result is directly compared to a table which describes the degree of success, from critical fail, to success at a cost, to complete success and critical success. You could assign absolute thresholds for those sorts of outcomes here, which I suppose is also a bit like Powered by the Apocalypse (with a 7-9 being a hit, and 10+ bestowing bonuses, and 12+ extra bonuses for advanced basic moves).

Make higher rolls better, assign absolute thresholds for levels of success

This was a solution used by (among others I’m sure) Fading Suns. In their Victory Point system, a player rolled a d20, trying to roll as high as possible while still rolling under the total of their applicable attribute plus applicable skill plus/minus any difficulty modifiers. The higher the roll, the more “victory points” awarded (per a little table on the character sheet), and getting more than an opponent matters.

This system also has some special effects for certain faces, though they differ from yours. If you roll exactly the target, that’s a critical success, doubling your victory points. In addition, a 1 always succeeds, a 19 always fails, and a 20 is a critical fail. (which spoils the otherwise elegant basic idea of “higher is better, up to the limit of your ability”, but still...)

A simpler version of this could work in your case, adjusting for the 2d6’s different probability curve (results in the middle of the range are significantly more likely). But it has the benefit of modelling that someone who is more skilled has a definite edge, as they are not only more likely to succeed but to succeed better.

Another example would be the Resistance Engine used in Spire and Heart; while the basic mechanic is very different (skill equivalents grant you extra dice to roll, and you use your highest single result), the result is directly compared to a table which describes the degree of success, from critical fail, to success at a cost, to complete success and critical success. You could assign absolute thresholds for those sorts of outcomes here, which I suppose is also a bit like Powered by the Apocalypse (with a 7-9 being a hit, and 10+ bestowing bonuses, and 12+ extra bonuses for advanced basic moves).