It might sound silly, but those chicken leashes might work? It could maybe help with him getting more sunlight? He seems relatively bonded to you and easy to pick up, but just in case your backyard isn't chicken safe, you can have him choose where he wants to be without worrying that he'll go into someone else's lot. I'm also wondering, does he get dirt/dust baths?
In the long run, it seems that if you can find him a happy home that needs a rooster that he can have some friends. In general, if you're spending all your time with him, I don't think he's really lonely. However, yes, he might want to be with a flock.