What does she do if you leave her without the wrap? Does she cry and generally not settle at all, or just roll around a bit get comfy and go to sleep eventually? I know my CHN says that once they're able to roll tummy sleeping is less of a problem because they're able to shift their heads to make sure they get good air-flow.

It's really sounding like short of using a straightjacket your little miss just doesn't want to be wrapped up. If you do try different sheets etc, have a look at Hip-Healthy Swaddling to make sure it's not too tight etc.