Hi!
The rules mechanics I have tinkered with based on polyhedral dice with shifts handles some basic things like this:
1. To hit and save mechanics
One of the additional things I don't like about single die systems its the inability to differentiate "evasion" (the ability to avoid being hit) from "armor protection" (the ability to absorb/deflect damage).
That is why in most single die systems there is little difference in the armor saves between infantry and vehicles or even between units of the same type. Nor can it easily handle distinctions between a nimble low armor target (high evasion, low armor) and ponderous high armor (low evasion, high armor) targets. usually needing extra rolls, modifers or tables to acheive this.
In our polyhedral system one roll is all that is needed to ascertain "to hit", penetration and a save.
Each unit would have a minimum of an Evasion value (EV), Armor value (AV), Fire Control (to hit) (FC) and Penetration Value (PV).
Let make two hypothetical elements.
A tank with EV: d6; AV: d10; FC: d8; PV: d8
and
An anti-tank infantry squad with EV: d10; AV: d4; FC: d6; PV: d8
All fire resolution is handled by the attacker rolling his FC and PV die and the defender will roll his EV and AV die at the same time.
All you need to do is compare values "at a glance" to know what happened.
If the firing players FC is equal or greater to the defending player's EV a "hit" is scored. If the PV is greater than the AV then the hit has penetrated and eliminated the defender (equivalent to failed armor save).
To make things even more easier and intuitive you can color code the dice (red for FC, blue for PV, green for EV and yellow for AV). The exact color do not matter. Any can be assigned. Human nature makes associations by colors far easier than remembering modifiers/values).
Using our fictitious elements, lets say the tank attacks the anti-tank infantry and the tank rolls: FC: (6) d8; PV: (3) d8 and the infantry: EV: (6) d10; AV: (2) d4
Since the tanks FC was equal to the infantry's Ev a hit is scored. The infantry element is eliminated since the tanks PV exceeds the infantry's AV.
All this is known with one die roll from each player rolling the appropriate dice type.
How would die shifts impact this?
Lets say the infantry is in cover in our example. It could be deemed that the cover is "soft" and they get an advantageous die shift increasing the infantry EV die to a d12 (one step up from d10).
Lets also say on that roll the player rolled a 7 (instead of a six), that would mean the tank missing due to the cover.
Or lets say the infantry is caught mired in a swamp or other difficult terrain meaning they are easier to hit. This could be represented as either an advantageous shift for the firing tank element or a disadvantageous shift for the infantry's evasion (it would amount to the same thing).
Note that this is a very simple "black and white" use of this system. You could attack many additional interpretations to the die roll combinations if desired. For example a "miss" with a successful penetration roll could mean intervening cover is destroyed, or a hit with no penetration can cause a "suppression effect" where the FC of the suppressed element can be impacted.
The permutations of this are many and serve to eliminate extraneous rules since the die themselves can tell you what happened depending on the combination rolls.
This system can be applied to all aspects of the game (morale, close combat, etc). I have some working systems for most of these.
Stat generation should be the last step since a sound die mechanic tied into the rule mechanic basically make the stats easy to do.
Of course, a points system for this is a topic onto itself.
Primarch