Players can spend coin or rep to take additional downtime actions for more healing as well. Not always what you want to spend on, but sometimes necessary. Our GM let us do an acquire asset to have an oncall doctor to assist in healing too. Finally, I think out crew grabbed a piece of turf that assisted with healing, but that part is a bit fuzzy.

It's easy enough to say that all wounds drop one level per Downtime phase. It's equivalent to filling the Healing clock once per downtime. Players can always spend additional actions to heal faster.

I agree with your assessment that wounds fun to hand out, but the cost of removing them makes me think twice about doing so.

I'm assuming we're talking long term injuries and not just mid session HP.
I'm also assuming you want something more efficient for maybe a shorter downtime, but not something they carry with them all the time.

Invent a "bacta tank" thing, something that makes sense for your world, and give them access to that?

Maybe it's a magical pool of healing in a long lost cave that's powered by a beam of moonlight.
Maybe it's powered by some offering or sacrifice to a divine (or darker?) being.
Maybe it's a particularly proficient doctor who uses new methods.
Whatever, since you created it, you can fine tune the healing vs resource cost exactly how you'd like.
Maybe a an hour/day/week in it refreshes x/y/z, it might be static amount or dice based. It might require some material or not.

Whatever it is, I'd make it location based just to be sure they don't haul that thing across all your future dungeons for infinite healing shenanigans.
Having that thing is their stronghold (if they have one) would be nice for sure, and maybe it'd make sense for them to build a sort of homebase around that magical place, but moving it around should be either impossible or highly costly, long and complicated.
Otherwise it's gonna be a bunch of shenanigans and they're gonna have that thing hauled by servants through the dungeon so they can refresh between every encounter. Or they're gonna bottle it up for sale and become BigFantasticalPharma or some other random PC idea.

Whether it's a place or an NPC, they'll likely become very protective of that, probably wanna keep that a secret and it can become a plot hook in itself.
"Sure... the blacksmith's daughter has been kidnapped, but — wait they got McDoc McShizzleWounds? Letsss gooo^oooo!^"

"The misty fog is weird, sure and people have been disappearing... we could investigate that maybe, but — what? there's a very remote chance that the fog is impeding the healing pool? Ready the horses! /clop clop"

Whatever it is, you're in control of exactly how much it does, you just need a believable and fun excuse.