I've got a couple of thoughts. First off, make sure the chicken is treated for every type of bug/worm early on. I have parrots, and find Moxidectin Plus to be a great cure-all for those types of things. It kills all parasites, inside and out. Chooks apparently don't like the taste, but if you add some orange juice to the water, I've heard they are okay with it. Just follow the directions on the bottle if you choose to use Moxi. If you don't want to use that, just use whatever worming and anti-lousing products you prefer.
The next thing I'd suggest is that you might want to add a special "dust bathing" area which you can control, rather than have her tossing wood chips everywhere all the time. I was thinking of a large plastic container, something like a small kids' pool or sandbox, eg. as on the following website.
https://www.walmart.com/browse/toys/sandboxes-water-tables/4171_14521_133062
I'd suggest putting very coarse sand in it for them to dust bath in. That way, they would still feel like they're getting a type of dust bath, but you wouldn't have to put up with actual dust from it since coarse sand won't fly all over the house. With it being contained in a smallish area, i.e. kids' pool or similar, you shouldn't get too much mess from it.
As for dander, I've had many indoor parrots over the years, and still do, and I haven't found it to be unbearable at all. You are obviously a clean person, so clean as needed and I'm sure you'll be fine.
Best of luck. I'm so glad you saved the chook.

I love a happy ending.
