Attempt number one:
It didn't look too tight at first, but after about 20 minutes or so it was obvious that her breathing was labored.
Attempt number two:
This went MUCH better. One, she was a lot calmer. We put a towel under her feet on the kitchen counter so she didn't slide around, and very gently took off the old wrap and re-installed it. Most of its self-stick was gone, so we put a few pieces of medical adhesive tape on it. It went on without a hitch, wings are in the right spot, and she's a lot calmer now.
If you're wondering, everyone is panting because the brooder light is too hot. I turned it off right after this and all is well.