Yes, I meant to suggest offering sauerkraut plain before you bother doing anything more complicated with the sauerkraut. If the hen likes it plain, great! If not, at least it was easy to try.
If you can find it, yes salt free might be best. Otherwise, just get whichever one has the least salt...
Personally, I would start by offering some plain. If she eats it, that is by far the easiest way to do it.
If she doesn't seem interested plain, then I'd try one of those ideas.
Would it be this one?
https://www.backyardchickens.com/threads/i%E2%80%99m-thinking-this-isn%E2%80%99t-going-to-turn-out-okay.1324428/
(I did a search for the word "screw" in posts by you, and then looked through the pages of results until I found something similar to what you had mentioned.)
If you decide to try having the vet remove the screw: I suggest another x-ray first, to see if it has moved. Things sometimes come safely through a chicken's digestive tract on their own.
I do not know how likely it is to resolve itself, but x-ray is a rather non-invasive way to check on it...