The short answer is "nope, not off the top of my head. Somebody smarter than I am is gonna have to figure that out."
The longer answer would be 1) think about paring down rather than building up 2) to look at reward structures in other mediums.
1) Super Meat Boy I think is an example of paring down. That game would just plain old suck if it had a lives system, and would probably suck also if it had a hitpoint system. Its gimmick is challenge+mastery (you either clear the stage or you don't, and you need to master gradually harder skills to clear later stages). So sure, there's some boolean value somewhere (you're either alive or dead), but it feels less hitpoint-y than, say, a Metroidvania. Heck, even Super Mario Brothers (lives system aside) does more interesting things with its trinary hit point system (big, small, dead): there are some routes through the level that are only possible if you've been hit. So I agree that hiding your hit point replacement behind a bunch of other complex factors would be too opaque and player-unfriendly, but that's not the only way forward. Not all numbers have to act like hit points. Not all hit points have to act like hit points! A metaphor that you may or may not find satisfying is that just because images on the screen are made up of pixels doesn't mean that every game has to be pixel art. We can build abstractions on top of internal numerical representations that are both expressive and usable.
2) Part of the reason why this is a manifesto rather than a design document is because it's utopian. I allude to it in the original essay, but I think we need to go spelunking for verbs from other places. Your question supposes that the player needs to die: that there needs to be something that ticks down that makes the game over. Books don't (usually) have that constraint. Neither do movies. The natural argument that I can come up with for why those media are different is that a game = winning/losing = win/loss condition = internal state= number related to internal state = something hit-pointy. Each of those logical links seem pretty strong, but I think if people push on them (or make explicit design constraints to go around them) there are plenty of non-conforming spaces there. There are twine games that keep track of internal states (player location/preferences/narrative progression) but have nothing that looks like a hit point. Portal is an example where you literally have hitpoints somewhere in the engine, but they have very little practical importance (they just determine how long you can withstand turret fire, say).
Bonus 3) I'm interested in how far I can push game design before I run into the "it's all gonna have to be numbers somewhere" limit while still making something fun. At the very least it would be a fun design exercise.
I apologize for writing the word "no" via several hundred words that were not "no."