The rat/mouse never has a chance to wake up early. I stun, then offer by tongs or fingers (in a glove) as they "twitch", and they'll strike and constrict. If they have no interest after about 20 seconds, I'll offer it to the next snake. I never let the rat/mouse out of my hands unless it's into the snake's mouth.
As for the bitten burmese, yeah, he recovered nicely. I didn't have to make him a helmet.