For Lunars there's an Intelligence charm in Glories of the Most High (the name escapes me), that allows you to mold flesh (yours and others') like clay. It can even be used to fix Crippling injuries. That charm and some logical custom charms expanding it allow some decent Lunar healing. You could also possibly build off the Lunar charms that let them 'share' their abilities, by letting a patient eat some of the Lunar's flesh and gain his superior regeneration. You can also do some nice medicine with Alchemy and by summoning demons and elementals, and lets not forget the Lunar ability to create anti-venoms, etc., with their Stamina charms.
As for how I handle Healing and Training times in my game, I use them more or less straight up. When time is important and every minute is being tracked I'm fairly strict. Being hurt is supposed to be a Bad Thing, and it makes Aggravated damage and various other effects really unappealing, which in turn can prompt players to surrender or run away rather than suffer them. I like this, and consider it more realistic than trying to fight to the death every time, which is an exhausting habit to deal with as a storyteller.
When the game is in full dramatic time, though, I tend to handwave away healing and training time. You need 11 days to fully heal and only have 10? That's fine, you're fully healed anyway. Might not have quite enough time train for that charm or combo? If it's essential for the upcoming fight, you get it.
It's a fine line to walk, because training and healing times should mean something, just as healing charms and training charms should confer some benefit. I err on the side of following the rules by the letter, because then everyone knows what to expect and doesn't just have to deal with ST fiat.
You can dare to do anything and succeed in anything, provided you never forget that two and two do not make four; in clumsy hands, they often make three or even less; but they can make five or six. - Louis-Herbert Lyautey