Minions in 4e ran the spectrum from level 1 to 30, had slightly better defenses sometimes to compensate for the 1 shot kill, and there were other things about them that I believe would be hard to incorporate well.
The idea behind them was always to simplify book keeping though for the DM, that you could use in 5e pretty easy.
Things I have done, not worry about the last few h.p of monsters, if a solid hit drops a monster to single digits and it would be fun to just have it die I let it die. Example the cleric attacks an orc that has been hit before and drops it to 7 h.p, if the cleric doesn't get many kills normally or if the combat is dragging out a bit, I just drop the orc to 0 h.p. Full disclosure I have optimizer type players so normally boost h.p a bit in the first place so it is essentially deciding to take away that extra cushion.
Another thing I have done is taken from 13th Age and their mooks (like minions), and that is for the little guys in a big fight just pool the hit points for groups of them. You have 5 goblins in a fight and they normally have 7 h.p each, the group has 35 h.p. Every time 7 damage is done a goblin dies, so if a fighter does 22 points of damage in an attack he kills 3 goblins. I don't do this often but it helps speed up large fights and gives a cinematic hero vs the horde kind of feel.
There is also an official variant on pg 272 of the DMG, cleaving through monsters.