Train, Release, Store in PC

[ReKoil]

Train Salamence, Release Noivern, Box Dragonite

Cloyster, Walrein, Dewgong

 

[RadEmpoleon]

Train Cloyster, box Walrein, release Dewgong

Breloom, Amoonugss, Shiinotic

 

[ReKoil]

Train Breloom, Box Amoonugss, Release Shiinotic

Sunkern, Skiddo , Capsakid

 

[VisionofMilotic]

Train skiddo, store sunkern and release the pepper.

The next one would honestly deadlock me...

Bulbasaur, Sprigatito, Treecko

 

[ReKoil]

Box Bulbasaur, Train Sprigatito, Release Treecko

Shroodle, Varoom, Glimmet

 

[VisionofMilotic]

Just going by design because I haven't used any of the three, let's train Glimmet, store Shroodle and release Varoom.

Male combee, a snom that can only be healed with herbal medicine, or a level 100 metapod.

 

[ReKoil]

Release Male combee, Train the snom that can only be healed with herbal medicine, Box the level 100 metapod.

Snom doesn't seem to be restricted to not evolving, since you can literally evolve happiness/affection evolution mons in a single camping session in Sword/Shield, given that they get Exp for playing with them at the end =D I'd just go camping straight away to evolve it and then heal up Frosmoth with the herbal as necessary afterward =3

Medicham, Throh, Crabominable

 

[VisionofMilotic]

I count camping as healing since you recover health in a camp session, so it's forbidden along with the pokemon center and all non-bitter medicine. Still, even without camp, you could maybe evolve snom with enough levels upsfrom rare/exp candy to raise its happiness. So agree, probably your best bet anyway.

Train medicham, store throh and release crabominable

Shedinja, ditto, smeargle

 

[ReKoil]

Release Shedinja, Train ditto, Box smeargle

Aron, Rockruff, Rolycoly

I count camping as healing since you recover health in a camp session,

That would be the result of cooking a curry. You can camp without cooking.
Just camping and playing with your Pokemon with the toys only gains them Exp. and affection/happiness, without them being healed. I literally just did this with my injured breeding Coalossal to doublecheck I'm not misremembering.