You could modify the healing table by making the edge vitality ADD to the rol instead of needing the required 6 on the drama. For NPC's you can let drama decide when they are healed and other such effects. For PC's however it gets more tricky-you don't want to have a bed ridden PC for a whole mission or worse yet for several episodes. I'd allow quick "dramatic" healing for them usually requiring the intervention of the other PC's.
Allow anywhere between an hour to a day between healing attempts (in-game of course), less if the situation warrants it.
If you want you could also have lingering side effects. Such as chronic pain, a medical problem or a drug addiction. I remember when one of my players had a terrible series of roles and stepped on a houdini mine. Everyone including myself thought he was dead-I managed to roll very very low and he barely managed to survive. He received immediate treatment and I gave him chronic pain since this was a miraculous situation. He spent the next episode in sickbay though he still took part in it.
"The misery of being exploited by capitalists is nothing compared to the misery of not being exploited at all."
-Joan Robinson, economist