🤔 Have you checked her vent thoroughly for the presence of lice, mites or maggots? Just thinking out loud here, but you mentioned messy tail feathers and it's obvious something is irritating her ... How about you give her a nice bath (that area, anyway) with warm water with a little Dawn dish...
I assume you have other chicks and she is the only one doing it? Perhaps her dirty vent is irritated and pooping irritates it even more. If it were my chick I think I would wipe a little petrolem jelly on her vent to soothe the irritation, morning and night for a few days and see if that helps...