My biggest issue with roll-over mechanics is the prevalence of Difficulty Class. In the end DCs are arbitrary because they rely on the whims of the DM instead of the mechanics of the game. So my goal was to make a roll-over system without DCs. But Delta of Delta's D&D Hotspot beat me to it with his Target 20 system.
Target 20 is intuitive and simple. The main mechanic is:
d20 + level + modifiers ≥ 20
That's it! Attack Rolls, Saving Throws, and Skill checks are based off this simple mechanic. But there's a caveat.
Delta did the math and came to the conclusion that Target 20 deviates by "1 or 2 pips.". In other words it deviates by 5% or 10% from the system it was based on. This deviation is positive for the most part. PCs take a hit to their early level saves, but they "closely match the book at middle levels; and are more generous at the highest levels." DMs might scour at this, but this deviation is also positive for monsters. So there's really nothing to cry about.
Target 20 was based off OD&D. So it will need to be tweaked to fit GLOG. The +level approach wouldn't suit GLOG because Attacks and Saves are made with secondary scores. Also it would be easier to modify the target number 20 with Defense than adding/subtracting it from the roll itself. So to hit an opponent with a Defense of 11, you'd need to roll a 21 or higher (because 11 minus 10 is 1.) Also the micro-math natural to GLOG needs reduction or elimination.
This is my first hot take:
d20 + Ability Score ≥ 20
d20 + Attack Score + STR/DEX ≥ 20 + Target's Defense
d20 + Save + CHA ≥ 20
d20 + 12 + DEX ≥ 20
d20 + 5 + DEX ≥ 20
I haven't figured out Opposed Checks or Combat Maneuvers yet. But I figured most situations are resolvable with a roll-off. A success wins. In the case of a tie, the highest roll wins.