I'm not going to be able to supply a tale of cheer our son didn't sleep through the night until he was 3 and not consistently until he started school. Same pattern as the OP - constant waking, demanding chest/bottle bright as a button at 6am the next morning.
We should have done the controlled crying thing more consistently but, frankly, it was easier to just microwave a bottle or shove a nipple in his mouth and know you could get another 1 or 2 hours sleep. When we did try it my wife couldn't really cope 'He's distressed'.
When he was born we told the placenta was slightly calcified but no more than that. We recently found out this may have meant he was getting enough nutrients in the last stages of pregnancy and was constantly 'hungry'. Even now (he's 17) he gets very agitated if there isn't a meal available when he was expecting one.
One thing, when you're both tired and stressed and it's 4am it's easy to fall out over trivial things. We had a 'what's said in the night stays in the night' rule - it saved a lot of day time stress.
Our daughter was far better.
One thing: They both slept on their fronts. Our son wouldn't even be put down on his back. We looked at he risk factors (income, smokers, type of property - all significant markers) and we were very low risk.
The best bit;
Wait 10-15 years (I know, but you have to play the long game as a parent) when it's time to get your teenagers out of bed for school you can walk into the room, bright and breezy, throw the curtains open and spend 5 minutes chatting to them in an animated way whilst they lurk under the duvet muttering swear words. I loved it