We had this with DS2 also. Was awfully tough, he just would NOT be put down day or night. Hated the buggy, swaddling would work for 30 mins only.
We slept with in shifts. taking it in turns to sit up with him in a sling on our chests until he was 9 weeks old.
I then, by accident whilst winding him on his tummy across my knee, discovered he would sleep beautifully on his tummy. Looking back I think he had mild reflux.
so, at 9 weeks. I took the plunge, bought a babysense monitor and put him down on his tummy.
I am NOT recommending this, I know it goes against all the guidelines. I didn't feel comfortable with it, the monitor helped a little. But I felt the risk of us falling asleep with him on us, and him suffocating was higher than the risk of him asleep on his tummy with a monitor. We were seriously, seriously tired by then...what with shfit sleeping, night feeds, teething toddler DS1.
Anyway, I just wanted to sympathise because it's very hard I know.
xx