There is no need to change his diaper until he finishes pooping. I've had this experience with several babies over many years. I helped to care for my baby brothers and I can even hear my mother tell me to wait until he finishes before you change his diaper.
If he's screaming during this time then I suggest that there may be something medically wrong and I would take him to the doctor. Or, perhaps he's screaming because you are holding him on the changing table anxious for him to finish?
Don't even pick him up at the first sign of a poop. You can check to see if he's finished by pulling back the diaper and taking a look. If there's not much there walk away and leave him to work on it on his own.
Why do you think he'll get a rash? Have you tried waiting until he's finished? Unless he has extremely sensitive skin he will not get a rash in the time it takes him to finish pooping, even if it's an hour.
If you think that the acidity is bothering him, apply diaper cream after every change. The cream will keep the poop away from his skin.