Goes to sleep in my arms gently rocked and sung to and is put down asleep
I would work initially on how your LO goes to sleep, because this is likely to be the main problem here.
Some basic sleep biology: people (babies and adults) sleep in cycles and between each sleep cycle we rouse slightly from a deep sleep and do a semi-conscious 'environment check'. In an adult this may be a simple shuffle around the bed, an unconscious glance at he clock and straight back to sleep. Historically it is a way to check we are not in danger whilst sleeping.
Babies do this too. They will have an 'it is safe to go to sleep' trigger - which is usually directly linked to what they need/do to get to sleep in the first place. If his 'it is safe to go to sleep' trigger is being in his cot, with his teddy/dummy (or whatever) then it is likely that he wouldn't even wake up at those environment checks. He'll just feel for his teddy, suck his dummy, shuffle around (maybe murmur a bit) and go back to sleep.
If at every sleep cycle he is stirring slightly, realising he is not in his 'it is safe to go to sleep' position (in your arms, being rocked) he will freak out, cry and ultimately fully wake himself up. Then you get him back to sleep (by rocking him in your arms). And so the cycle continues.
So I would recommend your focus needs to be on getting him to go to sleep in the cot, without being rocked. Very much easier said that done! It is unlikely to just happen, it may take some time and some gradual changes.
If it was me I would have the cot next to my bed. I'd remove furniture to allow this, if needed. I would remove one side off the cot, easily done with an allen key. I would butt the cot up to my bed. I would ditch the sleepyhead. I could cuddle right into that cot from my bed.
I would breastfeed, into sleeping bag, straight into the cot. Baby will cry because he's not used to this. But you are there. Cuddling right into the cot. Cuddling up and around him. Shushing so he knows you are there. Stroking, patting. Cuddling in such a way so that it actively stills the baby, almost pinning him down so that he's not squirming around. Dummy in for comfort sucking, reinserting constantly (because with the best will in the world, a screaming baby will need persistence to establish comfort sucking).
Cuddling, shushing, stilling flaying limbs, calming, patting, stroking. Always, ALWAYS being there for comfort. But the vitally important thing is that baby is not picked up - that comfort for falling asleep happens entirely and totally with baby lying in the cot and you lying next to him.
Once he's asleep, I'd extract myself into my bed. Then repeat at every wake up. In time, gradually, he'll get more used to being 'Put Down' to go to sleep. lowly, gradually, you can do less fussing comfort to get him to sleep. Aim to gradually do less. But don't expect it to be quick. He may well still need your (gradually reducing) help to get to sleep past is first birthday.