I have similar condition. My baby is 1 mth old. He likes to suck so much. The feeding time is so long and seems no napping time at day time.
I am now trying to pump out the milk for him, he drinks much faster and able to fall asleep. I think i should have sufficient milk for him as each time I can pump from 80 to 200 ml.
But I am not sure if it's a suitable method or not.