Have you and your Dr talked about the possibility of silent reflux. My baby girl has reflux and ive learned quite a bit. Some of his symptoms sound like reflux. Fussiness, restlessness, poor weight gain.
Also I think that if you can get him to take naps and get plenty of rest then you will see lots of improvement. Your baby will have plenty of strength to nurse hard and long. There are hormones in our bodies that cause baby and mommy to relax.
Your baby's nursing should boost your supply but since hes a sleepy eater you should definitely start pumping. Pump in between feedings or pump right after feeding.