I've never tried anything like this, nor even had it suggested, which is odd, because I am addicted to tinkering with the rules. My take on the meaning of the question is this:
Your character makes an attack roll. To successfully hit, the character has to acheive a score over the opponent's AC. This much is old hat. What I think is being considered here is using the attack roll, plus all relevant modifiers, as a damage roll, also. If the attack roll exceeds the AC, then whatever that number is equals the damage done.
If this is too simplistic an explanation, let me know. The only problem that I would have with it would be that it would be hard to do a decent amount of damage at once. On the flip side, a low-level character with a small weapon, say a 1st-level wizard with a dagger, might actually off a--normally--tough opponent if the opponent's HP are low and the character gets a high roll.
A critical would still be a critical, regardless. Also, applying the strength modifier to damage after the attack roll was made--yes, use it as damage and to-hit modifier, or maybe switch to dexterity for all attacks--might solve the low damage score problem.
If you used the "armor as DR" thing, I'm not sure this idea would work. Then again, as the characters go up in level, they get better at hitting things, in general. So maybe in addition to the "no damage-die" rule and the "armor as DR" rule, you could apply something that was like AC as it stands, but call it "Avoidance Class", and make it get lower with heavier and clunkier armor upgrades, a constantly-applied penalty--"encumbrance"--to movement, so long as the armor is worn, regardless of whether the weight carried exceeds the maximum light load. These three ideas should close the circuit nicely. I haven't tested it yet, of course, because I just thought of it, so YMMV.
Does that help? I hope so.
Steve
P.S. Apparently my long-windedness has allowed someone to beat me to the punch, again. I did forget to mention that the heavier, clunkier armors stop a lot more damage, along with making casting even more difficult than in the PHB's list--I don't like wizards in armor.