I'd allow it to work with Gentle Respite. I think I'd allow it with Regenerate as well, mostly since preventing a creature from Dying is exactly what 1 HP per turn would normally do, and it could be assumed that it starts the "body part regeneration" as soon as the spell begins (not magically conjure a full brain after a minute of minor healing).

I think that anything that's a little more than just trying to slap some Healing Word on it should work, as the chances of a player having access to one of those options is still very slim.