10 weeks is still so young! Have you read The Happiest Baby on the Block? He talks about the 4th trimester, basicly it's just out of the womb but the baby still has the same needs as he had 10 wks ago. Your son is just acting like a baby. He is way too young for CIO. I wouldn't advocate CIO for anyone at any age as it's very stressful for them and teaches your baby you won't respond to his communication, but even the die hard baby trainers wouldn't recommend it for a completely helpless newborn.
I second the recommendation to try other types of slings, but some babies don't like them maybe you have one of those. I never used our Bjorn as it was too complicated for me. Have you tried a ring sling or pouch sling? I use a babyhawk mei tei now and have for several months. It may feel more like the Bjorn to him but may be easier to get him out of asleep.
Also, putting them down in the empty is bound to feel very isolating to them. Perhaps a rolled up blanket along the baby if you can ease him down? It's difficult. Mine was the same way. I watched a lot of TV in those days.
I don't know when my baby started cooperating with being put down but she slept on me (even at night) forever-well it seemed like it was forever at the time. Now, suddenly she is 17 months old. I know it can be frustrating but they are only that young and cuddly for a really short time. Babies are individuals and even if everyone you know claims to put their babies down and they happily drift off to sleep, you may have one that won't go for that plan.
Sorry if this isn't helpful. I found it helpful just to stop listening to others tell me what they should be doing and follow my instincts and at that age that meant naptime on mama.