I know you say all recipes are working but there is no way to make woven cotton. Only recipe attached to it is using 3 woven cotton to make woven cotton.
I see on the internet all over it says to use 2 string to make woven cotton inside JEI, it show no recipe and when you try that it doesn't work.

Dug through the recipes and there is nothing to make woven cotton except to use 3 woven cotton to make 3 woven cotton. That file needs to be updated, if you intended 2 string. Please update it.
I've update my file wovencottonitem_x3.json and changed it to string to make 1 woven cotton.

thanks ahead of time.

Fixed in 1.12.1b