Get rid of HP. Physical attacks damage your STR DEX or CON (defender choice), mental attacks damage your INT or WIS. Energy draining could affect STR, numbing and weakness affect STR and DEX, etc. If an average PC has a stat of 9, and starting PCs have HP of d4 to d10 (2.5 to 5.5 average) then halving all damage in the system gives you an appropriate conversion. (EDIT: Brendan pointed out my math was wrong. To have 1d6 damage weapons, you need stats in the range of 1-6. See first couple comments below. I would not suggest using 3d6 damage weapons and 3d6 stats.)
What about leveling up? Your hero should get tougher, right? Don’t raise stats, just reduce damage. Every character level lets you ignore the first point of damage per round, from any source. So a 5th level PC gets into a fight with one goober who has a 1d3 damage sword. Goober swings the sword, he can’t ever damage this PC. But get six goobers together, now you have the potential for up to 18 damage in the round, so this PC might take some hits. In reality the goobers won’t all hit and won’t all get good damage, so this fight is still probably safe. Get a 5 HD monster in there: if he deals say 1d8 damage it’s possible he can beat up this PC. If he blocked 5 points from goobers with swords and then got blasted with an INT attack, he would have no defense left this round against it.
Fireball causes 1d6 per two caster levels, so a 5th level M-U casts a 2d6 Fireball, which is going to do 7 damage on average. That hurts the 5th level PC since he can only absorb the first 5 damage based on level.
Also, poison gets delivered on a hit regardless of whether it gets past the per-round damage reduction. So weak poisonous monsters are dangerous at any level!
Let’s give a 50% chance to hit, or 11+ on d20. Armor gives -1 to hit per AC.
Fighters get +1 to hit per level, double damage on natural 20 and can wear armor.
M-Us get +1 to hit per two levels and spellcasting (can’t wear armor and also cast).
I don’t see a need for saving throws. A Charm spell causes WIS damage so multiple Charms will eventually knock down a victim’s defenses. But high-level characters will be resistant to low-level charms unless bombarded by multiple casters simultaneously. A death spell affects CON, petrification affects DEX, etc. Once you hit zero you get the incapacitation effect of dying or being turned to stone. Sleep spell affects DEX and INT but with low damage to each (which makes high level creatures resist it well).
The defender management of his incoming damage in cases where he can choose (such as a blow from a weapon affecting either his STR or DEX or CON) gives him some interesting choices to make even when he’s passively getting whomped. Removing saves streamlines the system by removing an entire rule and related spells / magic items.
What to do about monsters? We want to use as much monster material as possible with little conversion. Assuming monsters have INT listed, give them equal WIS. CHA is 9 (to their own species) unless the creature is described as especially suave (Rakshasa) or crude (Goblin). CON should be 9 unless the creature’s STR is given, in which case it should equal STR. DEX should be 9 unless the creature is listed as being especially fast or slow. It might be necessary to just list out the 6 stats for every monster. I’m sure this would take about two hours for the 1st ed. MM1 or you could just copy what’s in the d20 SRD and fill in the gaps.
Natural healing should occur at 1 point to all stats per day. If this seems too quick, try 1 point to one stat per day. Remember 1 stat point about equals 2 HP. Because of this, magical healing should apply to stats of the wounded one’s choice if he drinks a potion, or of the caster’s choice if it’s a spell, and probably a Cure Light Wounds equivalent should heal 1d3 or 1d4.
To keep track of the level-based damage resistance, players should keep a die out with the DR remanining face-up, or else note it on scratch paper. Generally a round will be short enough that everyone will remember if he got hit or not, and tracking the number is neccessary only if you got hit for less than your DR. If you didn’t get hit, no need to write it down, and if you got hit for your full DR then you know you’re vulnerable.
Here’s the problem: we traded away HP and negative HP and death and dismemberment and saving throw rules, and in return now we track damage to all 6 stats (though mostly it’ll be the first 3 physical ones). There’s a death spiral since as you lose DEX you lose AC, as you lose STR you lose attack and damage. Tracking these moving stats will be a pain in the butt, especially for high level PCs with lots of modifiers.
And the big one, we need to rewrite spells, magic items, and monsters (which is about 3/4 of the game).
I don’t think it’s worth it. But I’m throwing this out here because maybe someone will use it to make something better.