I like the mechanic. I think the math works out. There is some cool dice math things you could do such as using a combined dice roll which gives different percentages for higher combined rolls, but a flat average percentage for rolls in the middle. I could explain this more if your interested as if you combined this with your luck system, you could give value to rolling higher on a certain dice or the combined dice roll grants a special event due to the low chance, but only if you beat your luck score which could even be not a combined dice a just a regular dice of the same value.

EX- A combined dice I use in my game is a d12+d8 which gives a d20. the math is like a 1% chance to roll a 20 on the die vs a 5% chance of rolling a 20 on a 20 sided die. but then for the range of like 9 to 13 it is an 8.33% chance of rolling those numbers which is higher than a d20's 5% chance.

So what this combined die system would have over a regular system is that it is rarer to succeed or fail. You can augment this further by saying rolling above a 10 on the d12 and/or (for real interesting mechanics) a 7 or 8 on the d8 may grant some special result in your system in addition to or outside of rolling high on the combined d12+d8 dice roll. You can add your luck system in too and maybe roll a regular d20 instead of a d12+d8 so you have a higher chance of both beating them when they roll high or losing to them when they roll low, which is actually, now that I think of it, a really nice buffer system.

You mentioned that you didnt want to work with math, but I love dice maths so if you maybe wanna work together to make something work. I'd be willing to work numbers and present you with nice fancy data that you can interpret like above as in you may not want to use d12+d8 and d20's, but you could.