I’m temporarily dropping the “dead at – Level hit points” rule and adding a “mostly dead at 0 hit points, there are no negative hit points” rule.
When you’re at 0 hit points, roll 1d6 on your initiative order. If you roll less than the number of rounds you’ve been mostly dead (how many times you’ve rolled the 1d6), you’re all the way dead.
I was going to say you can’t use healing potions on the mostly dead, but I reckon Princess Bride proves that wrong.
Anyway, we’ll try this for a while, and see how it goes.
Note: I’m adding this rule because roll20 makes it harder for me to discreetly fudge my damage or attack rolls lower and keep PCs alive.