Hi Bindy
I have had three weeks of the exact same issue- sleeping in arms but not basinette. Currently I hold baby till she settles from crying, the put her on her tummy and rock the basinette gently. I also hold my hand fingers open on her back so she feels like she is being held. Once asleep (20 mins) I turn her onto her back. She is only a month old and if she is really crying as opposed to grizzling I pick her up and start over again. Also, I would still wrap her. Sometimes I leave her hands out of the wrap so she can lie with them above her head if she goes straight on her back. I dont wrap hands if I start her on her tummy. It really seems to comfort her dropping off on her tummy but I make sure her head is to one side and nose and mouth free and I dont leave the basinette till I have turned her to her back.