I wouldn't worry too much about your return to work. DS has always been cuddled to sleep, but at the childminder's, she puts him in his pushchair in a quiet room and he just goes to sleep - no crying, no protesting, nothing.
Friends have told me very similar things, that babies who don't sleep alone at home will sleep alone quite happily at nursery or with a childminder. The pushchair though could be a suggestion perhaps? If it's movement he wants that could help. But he is so tiny, please don't worry about it just yet. I know I used to get DS to sleep at about 9 months when he was obsessed with trying to crawl, pull up on the side of the cot etc, by strapping him in his pushchair and either walking around the block or just rocking it back and forth in the living room without making eye contact with him.
What sling have you got? Most good slings won't hurt your back at 3 months - a baby bjorn/tomy/generic one probably will.
You could also try a really gradual approach if you want to wean him off cuddling to sleep. So cuddle for now, then move to lying down with him on your chest, but don't walk around, then move to lying down in bed with him but with him in the crook of your arm, move to lying down next to him, move to lying down further away with your hand on his chest/back, move to standing next to the cot with your hand on him, move to putting him down and sitting near the cot, move to putting him down and walking out of the room. If he likes to look to check you're still there, but eye contact wakes him up too much, then mimic falling asleep yourself - let your eyelids drift closed (or just keep your eyes closed) and peek quickly every now and again to see when he's asleep (though you should feel him go limp and hear his breathing change)
Oh and I'm pretty sure most 3 month olds can't roll or look at toys, don't worry! Cuddling definitely will NOT stunt his development, babies evolved to be cuddled :) Carrying him a lot is the best thing for him - the most interesting thing for him to see right now isn't a lump of plastic, it's you and other people - he's learning to be a human :)