Some possible suggestions:
- Index Card RPG
- Black Hack 2E: it is roll under attribute but it is pretty easy
- Dragonbane: only potential issue for you is that it is d20 roll under skill, but it's a very beer and pretzels game.
If you want to lean more into Sword & Sorcery but can tolerate some "outdated game mechanics," I would check out Flatland Game's Through Sunken Lands. It has classes like The Barbaric Conqueror, the Eldritch Sorcerer King, the Spell Thief, and the Cosmic Champion. All of which harken back to Moorcock, Howard, and Leiber. However, these are mostly roll under attribute.
You may also want to look into NuSR games:
- Into the Odd
- Mausritter: you play as mice but the game is solid
- Cairn: probably your best bet of the NuSR games