This system is about grabbing a handful of d6s, rolling them, separating them into horizontal rows, and having each of those rows represent a monster. A row of d6s tells us everything we need to know to run a monster, we just have to find uses for all the pieces of information the d6s provide to us.
The key to making an efficient system means recognizing when a resource can serve multiple functions. In this case, the d6s are going to serve as both a measure of enemy health (hit dice come to mind) and as an "attack pattern".
In order to do this, each d6 is going to represent a part of that enemy (for example, a claw, head, or tail) with a health stat and an attack/damage stat. You can read a row of attack/damage stats as an "attack pattern".
(NOTE: This current methodology of reading dice applies best to Into the Odd, as it doesn't have to factor in chance-to-hit or attack rolls. This is what I'm using in my sci-fi Into the Odd-ish game.)
DAMAGE AND PART HEALTH: When a player deals damage to the monster, compare the damage to the Part Health. If the damage is equal to or higher than the Part Health of one or more Parts, that part has been destroyed: remove the die with the highest Part Health that is lower than the damage. If no parts were destroyed, subtract the damage from the die that has the highest Part Health, then turn the die so its Part Health matches the new result. This'll change the attack pattern, and that's good. Enemies tend to change their behavior when they get hurt.
(Optional Rule) Flinching: if a player ends up destroying the part that the enemy's about to use to attack before the enemy's turn, the enemy loses their turn. Adds a dark-souls-like poise feeling.
INITIATIVE: If you're rolling up multiple enemies, just use the top-down order of their stat rows as their initiative.
EXTRA NUMBER: Open real estate. Use this how you wish, or don't use it at all. When I tested my zombie game, I use this as the "headshot number": if a player rolls exactly this much damage against a zombie, it dies instantly. In a different test, this number instead represents enemy soldiers' primary weapons, consulting a d6 table. You could also create a rudimentary d6 monster AI table and use the "extra number" to determine which PC it attacks, etc.
DOUBLES: Special attacks, abilities, statuses, etc. This one is optional. I like to have a d6 table on hand so I can make enemies with doubles into something special. This kobold has two 1s in a row? It's a shaman! This zombie has two 4s in a row? It has a mutated bile-spit attack! This supersoldier has two 2s? It's a demolitions specialist! And so forth. This can be used as an easy way to distinguish an enemy from the pack.
Within a module, an entire statblock could feasibly be condensed down to this:
Zombie (X), where X is the amount of dice.
EXAMPLE: I roll up two zombies, each with 2 HD.
Zombie # 1 2
Part health 25 34
Attack Pattern 44 51
(looking at these two statblocks, I think up some 'personalities' for the two zombies. zombie 1 attacks consistently, but has differing part healths, so I'll say that it's a former soldier with some body armor covering certain areas. zombie 2 has very differing attacks, but consistent part health. I'll say that zombie 2 is missing a leg and loses its balance, so the "5" attack is when it throws its whole body weight at the player, and the "1" attack is when it has to recover its balance.)
-My players roll initiative and win: they go first.
-Player 1 swings their brick-on-a-stick at zombie 2, and rolls a d6. Result: 2. The slash only cuts apart the tissue in zombie 2's tumorous torso, dealing superficial damage, but reducing the strength of that part. I rotate the part die so that the "3" of part health becomes a "1". This has an effect on the oncoming attack: what was once a "5" has become a "3".
Zombie # 1 2
Part health 25 14
Attack Pattern 44 31
-Player 2 fires their shotgun at zombie 1, and rolls a d10. Result: 8. The force of the blast destroys the first part (the "2") and has enough damage left over to destroy the second part (the "5"). Zombie 1 is killed with a single blast.
-Zombie 2 then acts, and attacks player 2 with a slam from a now-weakened torso, dealing 3 damage.
-The round then ends, and the enemy attack patterns update. The die at the front of the enemy stat line gets shifted to the back. Zombie 2 now looks like this:
Zombie # 2
Part health 41
Attack Pattern 13
-My players roll initiative again. Player 1 wins initiative and goes before the enemies. Player 2 loses and goes after the enemies.
-Player 1 attacks with their brick-on-a-stick. Result: 4. They smack one of the zombie's arms so hard that it flies off.
Zombie # 2
Part health 1
Attack Pattern 3
-Zombie 2 now acts, and goes for one last attack, flopping towards Player 1 and dealing 3 damage.-Player 2 now finishes off the zombie with the butt of their shotgun, rolling a d4. Result: 1. Zombie slain.