Here's the thing OP, this question gets asked all the time on Mumsnet. And the reason, as a PP has said, is because all the safe sleeping guidelines are also things babies hate.
A newborn still wants to feel the way they felt inside your womb. The thing they want the most is to be against your body. They want to feel you, feel your warmth, hear you, smell you. They want to be curled up and cradled. Safe sleep guidelines say they must be flat on their back on a flat, firm surface with nothing in the crib that would comfort them. Debate rages over the safety of swaddling and they can only be swaddled until they are able to roll. Your baby will cry it's heart out being put to sleep according to safe guidelines. Most do. Mine would startle immediately, choke, vomit his milk, scream and cry and flail inconsolably. Hours and hours of effort and swaddling and white noise and rocking would get at most an hour of sleep out of him. It was horrendous.
So... what do you do?
You know your baby best. You have a feel for what is safest. Go with your gut. My baby would only sleep, like yours, on my chest. For the first fortnight my partner and I took it in shifts to sleep so that one of us could have baby on our chest where he was happy. Then partner goes back to work... what then? Well, I end up utterly ill with lack of sleep. I mean hallucinatory levels of sleep deprivation.
I turn to Mumsnet like you for advice. Pages and pages and pages of discussion on the matter. Everyone has the same problem, no one has a solution. Everyone is ill with sleep deprivation. It leads to PND. I was becoming genuinely angry. I couldn't cope. I was not a good mother to my baby in this state and it was not safe and not sustainable. I thought to myself, how is this safe sleeping. How am I supposed to ride this out?
After reading and reading and reading about safe sleeping, and after trying absolutely everything with my refluxy baby, including co-sleeping and swaddling and everything else under the sun I decided to go with my instincts. The minuscule risk of cot death when all other safe sleep guidelines were ticked off (empty crib, firm surface, no smoking, no drinking, I breastfeed etc etc) made me decide it was worth trying putting him to sleep on my front.
This is verboten!! You cannot put a baby to sleep on his front, my god!!! Well I did, and I didn't sleep properly for a week as I sat up watching him in his next-to-me crib. He has been able to lift and hold his head up from birth and I watched as he'd shift to get comfortable and turn his head this way and that. Eventually, out of sheer exhaustion I fell asleep.
He is now turning 4 months. I started him sleeping on his front at 2 months. He is a different baby and I'm a different mother since doing this. He sleeps 12 hours a night, waking twice to feed. He is so happy all the time and so am I. His reflux disappeared overnight.
I am not recommending you put your baby to sleep on their front (although this is what they are already doing on your chest except they are not in a stable position and could be more easily smothered).
I am saying, read the advice, go with your gut, do what works and what you are comfortable with.
Cot death is often a traffic mystery. We can only do what we can to avoid it.
We must also sleep.