Alright, how about switching from dice to cards. 24 cards, half critical, 8 each numbered 0, 1, and 2 damage. Each card also has a number 1-12, repeated once in the set.
Instead of rolling dice, draw that many cards. No replacement or reshuffling of cards until the deck is exhausted. That would prevent luck swings, pretty much. It'd be hard to roll poorly more than twice in a row. And you'd be compensated later from the good cards that remain.
Or to get silly, a bag of 48 damage tokens, 0, 1, and 2. Half critical. You could reach into the bag and draw the right number of "dice" and just sprinkle them onto the injured creature. :-)