I've been dusting her with DE regularly. She keeps tossing her head, and shaking it. We are going to candle her eggs, and if none are fertile, we are considering buying some chicks from TSC or Southern States, for her to be a mama to.It sounds similar to what we do.
We have a big coop and lots of nesting boxes and lots of hens and roosters, so we have brooder boxes we use to keep a broody organized. The boxes are about 2.5' tall, 3' wide, and about 6.5' long. We can set one of our double nesting boxes at one end (where there is a door in the lid), and the food and water at the other end (another lid door down there) and there is a little bit of space in the middle so the broodies (maximum two per box) can scratch around and stretch their legs. We remove the broody poo when we see it. It still isn't a great place to dust bathe compared to the rest of the coop and run, and usually broodies want a dust bath ASAP after the clutch hatches and we take the box away ... but it does give the broodies peace and quiet and keeps them organized on their own clutches so they don't get lost on the way back to their nest after a potty break.
I wrap the nest end in feed bags so broodies feel snug and safe. I put feed bags on the top so nobody poos on the broodies from above.
We do keep an eye on the hens to make sure they haven't been infested while they brood.
If you can quickly get your hen's bum cleaned up and maybe dust her a bit by hand (just regular dust from your chicken area) ... then give her a private space? The eggs can tolerate a bit of a break from incubation. But unless you give her fake eggs, she really might not be happy about letting you take her clutch to incubate artificially.