OK I thunk up a couple more options for "instant death" that are less harsh than "die at 0". It seems to me that the salient effect is that you want heroes to
die on their feet instead of bleeding out, but you want
one-shot protection because getting one-shotted is sucktastic and unfun.
1.
Bounce-Back: If you drop to 0 hit points, and you haven't dropped to 0 hit points since your last short or long rest, you can bounce back. You fall prone and drop what you are holding, but regain hit points equal to your level + your Con mod (minimum 1 point). If you've already dropped to 0 hit points once since your last short or long rest, you can't bounce back a second time, and you die. Particularly important NPCs might use this rule also (when they bounce back, they regain hit points equal to their number of hit dice + their Con mod).
So that one provides one-shot protection but only once per short or long rest. Falling prone and dropping your stuff is just a flavor element to hammer home that you are really hurting right now. I like it when heroes and boss villains get a little extra oomph over mooks.
It's not perfect one-shot protection because many enemies can make multiple attacks. A variant would be, you get knocked out for 1 round and THEN bounce back.
2.
Negative Hit-Points: Your hit points can go negative, down to negative your maximum value, before you die. For example, if your maximum hit point is 42, then you can drop to -42 and still be alive, but at -43 or lower, you die.
While your hit points are negative, you remain conscious. But at the start of each turn, your number of negative hit points doubles. For example, if you start your turn with -7 hit points, then you immediately drop to -14 hit points. This isn't considered "damage;" it can't be resisted, and doesn't trigger effects based on taking damage (for example, you don't need to make a concentration check to maintain concentration on a spell).
If you receive enough healing to reach 0 hit points or higher, you stop losing hit points. (TODO: Something about Medicine checks healing you, but not to higher than 0.)
The "doubling" here is meant to scale with level automatically: you're more likely to face monsters capable of dishing serious damage, putting you at larger negative values, so the doubling should exceed your negative hit points at about the same rate as it did when you were low-level and facing monsters that were only capable of dishing low damage.
It's also supposed to be scary. So you take a hit and now you're at -3, no big deal, continue to fight on. But next round you're at -6, and you take another hit putting you at a total of -22, and holy crap, you'll probably die the round after that because you only have 34 hit points so
NEED HEALZ!
This doesn't provide direct one-shot protection but it does make one-shotting pretty unlikely because of the math involved. It also has a dramatic effect on healing mechanics, because healing at negative is not only no better than healing at positive, it's potentially worse because if you don't apply enough healing to get the character up to 0 then they are not stabilized!
I worry that the math on this option is broken and would make PCs unkillable, or lead to situations where you "bleed out on your feet" which is not quite as heroic as getting stabbed to death.