Agreed, anything that worked as a combat-accelerator rather than a death spiral might be good. Rather than a natural 1, just expanding 'crit range' by one could work, for instance.
Or, this could be weird: crits override disadvantage - that is, when rolling with disadvantage, if either die crits, even if the lower die would miss, it's a crit. More likely to crit with disadvantage (desperation!) and advantage, both.
But, whatever, as long as it applies to both the bloodied creature, and those it attacks.