I think it would be more straightforward if you replaced the penalty to monsters with a bonus to PCs (to replace the ability score bonus). Admittedly, this doesn't mesh very well with the CB (though it is possible, IIRC, to manually edit attack bonuses in CB).
That said, I'm not clear why PvP wouldn't work using your idea. If I understand it correctly, player attack and defenses are reduced by a roughly equal amount, therefore PvP ought to work okay (the biggest loss would be no truly weak defense, and therefore an inability for casters to target that defense).
EDIT: Okay, I see the issue. AC ought to be reduced along with NADs and Attack. I'd recommend the following base:
Cloth +0
Leather +2
Hide +3
Chainmail +2
Scale +3
Plate +4
Admittedly, this makes heavy armor largely undesirable (why wear Chain if Leather is just as good with less penalties). Unfortunately, that's an inherent issue in removing ability score modifiers without substituting something in their place. The advantage that heavy armor grants is a high AC without high Dex/Int. You could make heavy armors more competitive by increasing their values by +1 (equivalent to a 20 ability score), but that still leaves Chainmail relatively useless (Hide armor has less penalties).
I've been working on an idea along similar lines (though my idea also reworks the 4e math a bit):
Ability scores no longer influence attack or defenses, and have a lesser impact on skills.
Distribute 13 points between the following four combat values. All values start at 0 and may not be raised above 5.
-Attack
-AC & Ref
-Fort
-Will
-Attack replaces your ability modifier when making an attack roll, though it does not replace ability modifiers for damage or secondary effects.
Expertise is either banned, or grants a non-scaling +1 bonus.
The damage/crit bonuses granted by magic weapons/implements are still important, and either those items should be distributed as treasure, or the damage and crit damage bonuses converted to inherent bonuses based on level.
It is the DM's choice whether the Attack modifier only modifies powers, or if general abilities such as basic attack are also modified. Powers that do not have either the weapon or implement keyword (Dragon Breath) have any attack bonus granted by the power in the attack line reduced by 3 (by 6 at level 11, and 9 at level 21), to a minimum of +0.
-AC replaces your ability modifier for AC. It observes the normal restrictions, such as not stacking with heavy armor.
Magic/masterwork armor bonuses do not increase AC.
-Fort/Ref/Will replace your ability modifier for the relevant defense.
Feats which boost defenses are optionally allowable, but should never be allowed to stack.
Magic neck items and masterwork armors do not increase defenses (other magic items that increase defenses are not recommended).
Skills use either your ability modifier, or your trained bonus, whichever is higher. The trained bonus is +5, with an additional +1 bonus per tier if the skill is on your class list. You can choose to be trained in skills that are not on your class list, although you will not benefit from the tier bonus. The Skill Training feat grants you a class skill; the feat gives you the tier bonus in addition to the trained bonus. Allowing backgrounds to grant +2 is not recommended.
I recommend an additional benefit to being trained in a skill, to make it a respectable choice even for players who have a high relevant ability score. I have a number of ideas, the simplest of which is to allow each trained skill to be rerolled once per day.
All of these values scale at a rate of +27 over 30 levels (+1 at every level except 1, 11, and 21). This replaces the +1/2 level modifier. You can easily change the challenge level of the campaign by increasing or decreasing the level modifier.
