White noise also helps Lyla fall asleep, so we've stopped using the sounds on the swing and started using the Sleep Sheep from her crib. I put it next to her on the swing so she becomes accustomed to its sounds.
I'm happy to say we seem to have accomplished this, or so far so good! We started by leaving one arm free for a few naps. At first her arm took on a life of its own and woke her a few times, but she has grown accustom to it. Babies naturally move a lot while asleep (the swaddle restricts this which is one of the reasons it is so effective early on). Today I put her down for a nap with both arms free- I wrapped her lower body as before to keep her warm, with some mittens for warmth and to prevent any scratching of her face.
I still don't know how I'm going to transition going down for the night from the swing to the crib. I've been encouraging more playtime in the crib so it becomes a familiar, more friendly place.
But I'm still pretty nervous, and am stalling a bit. To be continued. . .