It seems like your biggest hurdle running 5e games with OSR systems will be ability checks & monsters. Luckily, most OSR games' abilities are more player-facing. DCC isn't, but in that case you could use their Difficulty checks almost as-is.
Saving Throws. Instead of resisting dragonbreath requiring a DC 18 Dexterity Saving Throw, the player references their own dragonbreath save (Or whatever you use). This makes converting saving throws on the fly from 5e > OSR easier than the reverse.
Ability Checks. 5e uses a lot of ability checks. Ability checks have a lot of variety amongst OSR games, but IME these are also more player-facing, so if you just know what type of check to use, this shouldn't be too difficult to convert since you usually won't worry about converting a target number.
Monsters. 5e numbers aren't actually too far off from most OSR games IF you remove the modifiers to any monster stats, for example:
5e Orc (Original). Armor Class: 13, Hit Points: 2d8+6 (15), Damage: 1d12+3 (9)
1e Orc. Armor Class: 14, Hit Points: 1d8 (4), Damage: 1d8 (4)
5e Orc (Revised). Armor Class: 13, Hit Points: 2d8 (9), Damage: 1d12 (6)
Under this system, the revised 5e orc still has more hit points and will usually deal more damage than its 1e equivalent, but it has worse Armor Class (Armor Classes are mostly lower in 5e), and your typicaly 5e encounter will feature waaay fewer creatures than your typical 1e encounter.
Just for fun, let's apply this to the Tarrasque:
5e Tarrasque (Original). Armor Class: 25, Hit Points: 33d20+330 (676), Damage: 4d6 + 8d8 +4d10 + 4d12+50 (148)
1e Tarrasque. Armor Class: 23, Hit Points: 300, Damage: 4d12 + 7d10 (64)
5e Tarrasque (Revised). Armor Class: 25, Hit Points: 33d20 (346), Damage: 4d6 + 8d8 + 4d10 + 4d12 (98)
Similar pattern, even under this system the Tarrasque is still tougher, but we bring the numbers down into "more useful" territory. Definitely not a perfect system, but if you need to convert very quickly. Honestly, the 1e Tarrasque could use a buff anyways. DCC player characters are pretty tough too once they've survived a funnel.
Modified as I incorrectly stated the 5e Tarrasque's revised hit points would be 446.