Interesting... I have seen several of my broody's molt out their beards. Never thought about it having relevance to brooding. But I guess that kinda makes sense since they are nutritionally (likely) deficient after sitting for so long and some industry practices include diminishing nutrients to induce molt.
@MarySue So cool that you provide for your rooster as well!
I would just make sure you girl is accessing maybe the flock raiser as much as possible or substitute her with a little protein since feathers are made of 90% protein (or the amino acids therein).
A couple quick facts.. feather mites will NOT be seen with the naked eye. There are more than 1 type of lice on birds and you won't see head lice on the body (they are usually little specks around the eye).
Also, there are
very few worms that are visible in poo, so I wouldn't assume not to have them just because you don't see them.
And despite hanging out with lap girls for hours on end... I never saw anything until we were processing cockerels. The easiest way to see things is use your flashlight after dark, place bird on back, legs bent towards chest and part the feathers on the abdomen and the vent to see if anything is running away.
What did you use to get rid of you parasites last year? Some areas have much harder times especially during certain seasons.

Permethrin spray is an effective product that is easy to use, affordable, effective, and no withdrawal time for eggs if used as directed. There are organic versions if that's important, but they are way more expensive.
Chicks raised with broody's do not *usually* need Corid. But you know your situation better than I do.

Corid by the way is a thiamine blocker that slows the growth of coccidia (does not kill them) which are in every single chicken poo and ONLY become a problem if there is an overgrowth of them which is accentuated in warm humid conditions like that of a brooder. Maybe your old girl can't handle the reduction? But also, are you putting the vitamin supplement in the water or roosters' feed? If in the water then you *may* be defeating the purpose of the Corid and vice versa, the corid defeating the purpose of the vitamins.
IF you aren't having issues with cocci, I might discontinue the Corid use. And also note that unless your roo has issues, the flock raiser should be formulated to meet all of his need without the vitamin supplement. Although you can overdose on minerals that is not an issue with vitamins. However, if your body doesn't need them, it's just making for expensive pee.
Hope your girl feels better!