Hmmm... I have always had good sleepers, and I am sure part of it is just luck or genes... haha! But considering I have gotten poor napper daycare kids to sleep consistently, it can't be all nature. I am very consistent with routines and schedules as soon and as much as possible.
I am trying to think of suggestions. Does he eat ok? I mean, why does he wake up so soon after going to bed and eating, just to eat again? Is he really hungry? I know with my son being very small, we would have fed him as you are, but now that he is caught back up, we wouldn't.
Also, my son regularly wakes up in the middle of his nap. I have to be VERY specific with my family/friends who watch him, that they don't hear him wake up at 1:30 and go get him out of bed. He will babble for 20 minutes and then sleep until 3:00. He will do this some nights as well, brief babbling moments in the middle of the night. But it sounds like your son wakes up crying at 3am... Do you think spending a couple weeks letting him "cry it out" would be too much for your other kids to deal with? I know it would suck for a while, but I wonder if he learned that you were not coming right away, if he might not get up that early any more.
Also, see what you can do about naps. Sleep Begets Sleep. Usually the better a child naps, the better they sleep. I try to follow a routine with my kiddos, such as our big afternoon nap is immediately after lunch. For those that take morning naps, it is immediately after breakfast (we eat breakfast at 8:30 til 9:00... so if you eat breakfast at 7am or something, that might not be best). Now, I have no control over what my daycare kids have at home for routines and whatnot, but I have heard it dozens of times how much better their kids sleep at night after starting to come to my daycare. So that really supports the good nap = good nights theory, but it doesn't mean it applies to ALL kids either.
I have no clue if any of this will work for you. It has worked for my own kids as well as numerous daycare kids, but it can be challenging to "train" (for lack of a better word right now) a poor sleeper to get into a routine, but after those rough couple weeks, you will wonder how you did it before.
And I wouldn't think it is totally unheard of to have a sleep disorder at such a young age. If it doesn't improve, I would totally check into it! Best of luck! I really hope something works for you. I know I couldn't function with such little sleep, especially pregnant!