I wouldn't worry to much about volume being pushed through, hopefully you have someone helping and use the pump three times, stand on the pedal, then open the bleeder pretty far, keep pushing until it hits the floor method. That usually works the best. The only other thing I'd usually recommend is a pressure bleeder that goes on the MC.
Sometimes with test equipment at work we have to apply as high a pressure as we can by applying the MC and then leaving it for several hours. That seems to get the air out of crevices after you bleed again. Practically doing that inside a car is a little tougher.