OH MY GOSH!!! Her feathers are the most beautiful gray color I've ever seen!
My SG hen got egg bound once because she lays giant eggs.
Seems like you are doing everything u can. You're feeding layer feed, right? Not all-flock bc it doesn't have enough calcium for hens to lay eggs.
One time, last year, I switched my chickies to all-flock because I learned the extra calcium is bad for the roosters. Because of me my brahma hen Dottie got a prolapsed vent from the lack of calcium in her diet. Vet put a stitch in her butt to keep the prolapse in, I switched her back over to layer feed, and the issue has not happened since.
I bet she's eating the calcium supplement when you aren't looking, that's what my babies do idk why though lol!! Do you free-range your chickens? Not ideal but you could try giving her a calcium pill once a day if it continues. Here's a link for more info.
https://www.backyardchickens.com/threads/egg-bound-hen.1469528/post-24480682
You also might want to try creating a thread on this issue with your hen. I hope this resolves