I grew up in the 90's era D&D (2nd edition and BECMI) which was far more lethal than WotC era editions but had already drifted from the 70's notion of "expendable characters tossed at the dungeon" that most OSR movements aim to emulate. By the late 90s, a lot of our house rules looked very similar to what 3e and beyond would look like (lax race/class restrictions, no level limits, Max starting hp, resting restored most/all hp and spells, etc).
We started in the early 80s; and by the 90s we'd done some of this but not all. We'd relaxed the race-class restrictions considerably, removed most level limits, and increased rest benefits over what 1e gave you (though not to anything like 4e-5e have it!). Death was at -10; at anywhere from 0 to -9 you risked going unconscious and (unless right at 0) would bleed out and die if not tended.
We've never done - and daresay never will do - max starting h.p.; but we did add in the idea of 'body points' which, for the usual adventuring races, gave everyone somewhere between 2 and 5 extra h.p. to start with. (your body points do not change by level).
One thing I would love to see (and excuse me if it exists but I am unaware of it) would be some marriage of OSR aesthetics to a more modern mechanical system. Most OSR seems to want to grab the B/X or 1e style of tactical, lethal play that calls to the classic meat-grinders like ToH or KotB. It would be interesting to see someone do a take on how 2e tried to present the game (you are the protagonists in a fantasy story) but without the later gonzo of 3e and on (ubiquitous magic, strange races, post-medieval tech).
I don't know of any published systems that do this, but I can kind of see a path to homebrewing something that might work.
It'd start with the 3e/d20 chassis, but with the power curve greatly flattened to 1e-ish levels* and a lot of the 'gonzo'** stripped out. Skills would be physical or knowledge-based only; most social-interaction rules would come out. It'd be open-ended - no expectation of 1-20 play; a 2-year game might only go 1-5 and still be great - and it'd be able to handle any speed of advancement the GM wanted (i.e. the GM is encouraged to tweak the level-advance table). Either ban multiclassing or allow only two classes, independent a la 1e rather than additive a la 3e. Few or no prestige classes. Few or no feats, with some of them siloed into class abilities and the others kicked to the curb: the focus becomes on the in-play game rather than the character-build game. More guidelines around henches, hirelings, strongholds, and so forth. Monsters just become monsters, they don't all have levels in this or that like 3e does it; though specific individuals might.
Oh, and throw out the idea of CR/EL and replace it with decent guidelines for GMs on how to run non-combat encounters (could include morale guides etc.). Also, put more emphasis in the player-side materials that not everything is there to be - or even can be - beaten in combat. Xp comes from a mix of sources: combat, combat avoidance, treasure, mission achievement, etc.
* - thus making variable PC levels within a party a viable option, while also making various monsters viable threats over a greater span of PC levels.
** - use 1e's core list of PC-playable races and classes (maybe replace Paladin with Cavalier, design Bard to start at 1st level, and add in a spontaneous caster e.g. Sorcerer), strip out the tech (unless your story happens to need it), strip away a lot of spells particularly buff spells, etc. The one thing I'd keep is a relatively high amount of magic, as in OSR magic items tend to be rather important to a PC.
Is this on the right track, for what you have in mind?
