But then none of the other birds can lay there, so they'll develop the habit of laying elsewhere.Is it possible to break her broodiness by just blocking all of the entrances to the nesting box? I don't care if it takes a long time.
If you don't have a crate, do you have anything on hand that's big enough and secure enough to house a chicken for a few days/week? If not, a crate is a very good investment, now and in the future, if that helps justify getting one...