Re: Transitioning preemies to the breast
Welcome to the forum and congratulations on the babies and on breastfeeding them for 10 weeks! That's awesome, especially considering that they were such early birds.
Please don't worry about supply being "established" at 12 weeks. It's not true. It's a little easier to boost supply in the very early days/weeks of breastfeeding, but you can increase supply at any time, given the right stimulation. Pumping every 2 hours instead of every 3, pumping for longer, and pumping at a higher setting, combined with nursing the babies more frequently- that's what will get you where you want to be. More demand = more supply.
Throw the babies' feeding schedule out the window. At 4 weeks adjusted age, and a nice full-term weight, there's no reason to think that they will burn too many calories by nursing. Full-term babies typically nurse about 10-12 times a day, or even more often, in the first 6 weeks of life, so I think you want to aim to cram as many feedings or nursing sessions as possible into the day.
What sort of pump do you have? For a mom who is struggling to establish supply with a young babies who are not nursing all that well (e.g. falling asleep at the breast, being lazy at the breast if it's not really full), you definitely want a hospital-grade rental with correctly sized shields.
Coolest thing my big girl said recently: "How can you tell the world is moving when you are standing on it?"
Coolest thing my little girl sang recently: "I love dat one-two pupples!"