Believe it or not, a system like the one you're discussing already exists. Not that yours doesn't have some merits, but the one I'm going to tell you about is probably simpler to understand.
The system to which I refer is Sean Mirrsen's progressive die system, which I will copy pasta here. I'm not 100% sure when it was first used/suggested/created, but it can be found in a few places like
here and
here. I've always kind of liked it for a few reasons.
=== PROGRESSIVE ROLL RULES ===
For every Action a Player submits, the Game Master rolls a die to determine its outcome.
The number of sides on the die rolled is determined by the value of the skill or attribute assigned to performing said Action.
The outcomes are selected from a predetermined list, sorted by severity:
Epic Fail(EF): The intended result was not achieved, and the character suffers additional problems as a consequence.
Failure(F): The intended result was not achieved, but no further complications occur.
Partial Success(PS): The result is only partially achieved, with exact degree determined circumstantially by GM.
Success(S): The result is achieved, though the character may suffer unintended consequences.
Epic Success(ES): The result is achieved, and any consequences turn out positively for the character.
Overshot(OS): The result is nominally achieved, but the character suffers consequences from intentionally or unintentionally "overdoing" the action.
The table of outcomes is determined thus:
(Die Value):[Roll Value]-Outcome;
(D1):[1]-Epic Fail.
(D2):[1]-EF;[2]-Fail.
(D3):[1]-EF;[2]-F;[3]-Partial Success.
(D4):[1]-EF;[2]-F;[3]-PS;[4]-Success.
(D5):[1]-EF;[2]-F;[3]-PS;[4]-S;[5]-Overshot.
(D6):[1]-EF;[2]-F;[3]-PS;[4]-S;[5]-Epic Success;[6]-OS.
Above (D6), the outcome table is expanded by padding Success outcomes inbetween Partial and Epic Successes.
Thus, for instance, a roll of (D10) will look like this:
(D10):[1]-EF;[2]-F;[3]-PS;[4-8]-S;[9]-ES;[10]-OS.
As a rule of thumb, the severity of the overshots and epic fails will depend on the value of the die being rolled - so getting a [5] out of a (D5) is a much milder overshot than a [10] out of a (D10)
Basically, bonuses increase die size rather than result, leading to diminishing returns. Personally, I think enhancing all of the results might be better, not just overshot and epic failure. I'd probably add more perfect successes further down the line if I didn't do just that. Suffice to say that it is a versatile system, which is why I'm disappointed that it doesn't get used more. The main downside it that it warrants a random number generator, as I doubt many people own a d7/d9/d11. I mostly like it because it penalizes dump stats much higher.
Another downside is that contested rolls between two or more highly skilled/extremely strong things can be somewhat vague, as both sides usually succeed to some degree. Very few games would warrant rolling more a die larger than d12 though, so I feel it is passable in that regard. The system definitely fizzles out in effectiveness around the d20 though.
For awhile now, I've actually been considering building a modified progressive system that goes Epic fail, fail, fail, partial success, partial success, success, and THEN we start adding higher degrees of success. We would upgrade fails to partial successes, partial successes to successes, and successes to epic successes. There would be no positive overshot in such a system, but perhaps Epic fail would have it's own table. Such a system would mostly symbolize a d6 as the average, unskilled person's ability to do any given task. Going up to d8 or d10 would be someone who mostly knows what they're doing, and a d12 would be more professional. Of course, an rtd should always have a chance of failure, because otherwise there's not much point in rolling dice really is there.
The basic d6 is a good system on its own, especially in a minimalist setting, but adding bonuses and penalties to it defeats the purpose. 6 numbers or results is far too rigid to throw off like that, from what I've seen. Even a +1 bonus is such an absurd advantage under such a system that if one does a little statistics, either everyone has to minmax in such a system, or no one does. In most cases, a more complex game warrants a more complex system. That's not to say that there aren't exceptions, but those games are generally more exceptional due to the people that run them than the system used to run them.
Well, that ended up being a larger wall of text than I thought I would make, but I hope it'll be useful.
Edit: Another alternative could be a hybrid system, where both the die size and the modifier increase or decrease. I think that's what you're creating though, so carry on.