The only experience I had with a broken limb is one two NPCs. One of them healed in three days. The other one took pretty much forever to heal, so I just set his Limb HP to full with Debug mode after a week.
Only healing during sleep makes some sense to me. I don’t think a person should heal while their doing strenuous activity, but if you’re doing something like sewing or cooking or reading, it’d make sense to heal slowly. Otherwise, the only way to heal while awake is with Fast Healer/Very Fast Healer/Regeneration.
It seems like the problem here is that when a limb breaks, it takes a long time to heal. And that when you get hit on that limb, it completely resets the healing process, no matter how far along you were in it and even if the limb itself didn’t take any damage.
Perhaps reduce the time it takes to heal a broken limb? I know if I had a broken limb and had to nurse it on my own, I wouldn’t be out fighting zombies. Perhaps a healing time of three or so days on base?