Update that Carrots has been successfully wearing a saddle.
Despite separating at key times, she's absolutely determined to be near to the big cockerel. After he'd scratched off the stronger feathers on her back, it took almost no time for her back to look like this.
Some of you mentioned she could be getting pecked because the under-feathers can look yummy to other chickens. I finally witnessed that. Carrots is not the bird to stand for it, but chickens are quick. They were sneaking in a good peck here and there when she wasn't expecting it.
Of course, that happened when she was separated from the big guy, meaning the separation strategy wasn't as effective as well as I'd hoped.
I've never dressed a chicken so started with the most basic (least intimidating) saddle style: the piece of canvas with elastic wing loops. I somehow captured her one afternoon and slipped the loops over her wings, then fiddled with it until it was finally positioned correctly over her wings--chicken wing feathers are complicated!
She was separated in the coop run for 5 minutes to adjust, but it wasn't needed. She could care less about this thing. When I let her out, I threw scratch down so the flock would have something to focus on besides her new duds. They could've cared less, too. The neutral color was a good choice. She blends.
After scratch, she hopped on to her favorite perch to preen until the saddle fit even better.
Reviews warned the elastic may wear down sooner rather than later. We have 2 other styles with snaps and wing-protectors if needed, but this one is great for now, and it's not crimping her style. She's a chicken about town. She can still fly to my shoulder with no problem (callooh callay

) and can mix with the flock any way she wants. Also, I wasn't as worried about having a partially bald chicken when it was 11°F with 99% humidity a couple nights ago.