In many cases you can break them with bedding/litter underneath (that's how I do it, as my breakers simply sit on the ground) but it might not be as fast or as effective if a bird is really set on brooding.
A broody should stay in the cage day and night for optimal breaking. IF the isolation cage is not safe for overnight stay (i.e. sits outside the run, run not predator proof) then put her on the roost at night, and retrieve her from the nest box the next morning and put her back in the cage. It may take a little longer this way but better than letting a predator get to her.