Congratulations on your new additions! I did not read every reply to your OP, but three of my four babies were late term preemies (36, 35, 34 weeks). My BF experience with each was different, but ultimately successful. I'd definitely recommend pumping as much as possible to keep your milk supply up and store any excess for use later. One of mine was very sleepy and we would stimulate her feet and undress her and stimulate her with a cool wash cloth to get her roused enough to feed well. If she dozed back off we'd wake and repeat. We aimed for every 2 to 2 1/2 hrs from start of feeding to start of the next one and only let her have one longer stretch at night (more like 3-4 hrs).
Definitely consult a lactation consultant for help as well, especially if they are feeding better from bottle than breast. With one of mine I used a n*pple shield to make it easier her for to latch one for several weeks. With another we used pumped breast milk in a supplemental nursing system to keep a slower, but steady supply. There are lots of things you could try that may help.
Blessings,
Beth