Quick thought:
What is saves just had a single task resolution number on a d20? Base 15. Lowers by 1 per level after first. Add your appropriate attribute modifier. Fighters get an extra +2 against strength and constitution based saves, specialists get +2 against dexterity and charisma based saves, and magicians get +2 against intelligence and wisdom based saves. You could also use this system for raw attribute checks and not just saving throws when its something more general and not in the realm of a specific skill, instead of the commonly used "roll under or equal to attribute" mechanic.
Thoughts?
To make sure I understand...so if poison gas is sprayed at a first level fighter, she will roll a d20 and has to get higher than 15. She will add +2 (I assume poison is a CON thing, although the spray could also be avoided with DEX). If she had a 14 STR, she would add another +1 to the roll. She would need to meet or beat 15 to save vs. the gas. If she was second level, she would need to meet or beat a 14.
I think this would work fine. There are some systems (Numenera, Pathfinder...Savage Worlds, I think?) that use this for skill checks but the Referee assigns a difficulty to the task.
If you want "all high rolls = good" in your game, the publisher was considering at one point changing skills to requiring a 7 to succeed. You would roll a d6 and add your skill points to the roll. This would maintain the exact same chance of success vs failure, but flips it so that high rolls are desired.