d20 - fighting styles

[Blue]

Just noodling around an idea and looking for feedback in context of d20 type games.

Fighting two handed, vs. two weapon, vs. sword and board, vs. hand free are often built into character concepts, but end up having a lot of mechanical time spent on them. What about a simplification like this, requiring no feats/fighting styles or anything:

Weapons have a generic die of damage set by class, call it dW. So a fighter might be d10 and a wizard d6. (5e HD size would make a decent equivalent for a thought experiment.)

Weapon: 3dW + modifiers. Hand free.
Two handed weapon: 5dW + modifiers.
Two weapon fighting: 4dW + modifiers + overkill.
Thrown/one handed ranged: 2dW + modifiers (short range) + Hand free
Rapid thrown: 3dW + modifiers + overkill. Double ammo use.
Two handed ranged: 3dW + modifiers (long range)

Special
Hand free can either be used for something like a shield, or if empty is +1 to hit.
Overkill is any leftover damage get applied to a second target. It is a mechanical sop to having less wasted damage past what is needed to drop when you could potentially redirect the second attack elsewhere if the first drops an opponent.

"Rapid thrown" is the equivalent of two weapon fighting with throw weapons. Useful for archetypes like knife throwers.

Speeds things up by just needing a single attack roll, and no oddities like bonus action attack (5e) or full round attack actions (3.x) to deal with.

Yes, the dice are much larger in proportion to current D&D type modifiers. And total weapon damage is much higher than D&D without other boosts. Let's not worry about that right now, that's another post.

 

[Blue]

Overkill seems like an easy solution to having to make multiple attack and damage rolls, perhaps each with their own math (this one has a +1 sword, etc.) but how to handle when there are non-damage effects, or even a foe that has Resistance to the damage type of one weapon and not the other.

I'd be okay with conditions ("Poisoned condition for 1 min") going to one. But how to deal with, say, one weapon granting 2d6 extra fire damage and the primary target (who dies) is resistant to fire. Do we just go the simple route and it's just the leftover damage? Because unravelling it gets rid of the whole simplicity of Overkill. But what about the other way - if I land a big hit on a wimpy creature with a pair of slashing weapons, and then the extra damage is going over to a creature with Resistance to slashing, giving the whole damage seems wrong.

The more I look at it, the mechanics of overkill have a lot of odd corner cases.

So, how would you stylistically do two weapon fighting without separate attack rolls?