sorry, i'm kind of confused at your description of moving/adding files to the binder. are you using these things? each document has its own label...?

edit: wait i think i understand now. i'm not sure if this'll work for you but back in high school i used to use those thin sticky notes that people use for marking up books. i wrote my own label on that and stuck it on the first sheet of the section as a makeshift divider. it's a little janky haha but it's nice because you can move its position pretty easily so your binder won't look wonky

edit again lol: here's an amazon link to something similar to what i was talking about!