Thank you all for the helpful advice. I made a sling for him, which he used for about 20 minutes before he decided that it was enough and let out a grumpy bawk and somersaulted out of it. I caught him before he could hurt himself and set him down on the floor. He took off running and flapping to a towel I had on the floor. I'll try to redesign it so he can't do that again and slowly try to get him used to it.
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He gets daily visits from the two chicks that in the house brooder. During today's visit he decided that the towel they were on wasn't good enough and tried to fly to the couch. I helped him up and he preened and took a nap.
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Everyday he seems stronger and harder to keep immobilized.