How well feathered are the babies? if they are pretty well feathered they don't actually need to be in a box. The amount of warmth they require reduces as they get more feather coverage. If you're worried about the warmth issue you could try putting a heating pad on low under the tray of the cage directly under the box you put the chicks in on the floor. Hopefully it will reduce your pair's drive to breed. It won't be like a nestbox exactly. If the chicks are 3 or 4 weeks you could remove them and the box and hand feed! They should be down to 4 or 5 feedings a day at that stage and don't require feeding overnight. Kay Tee Exact handfeeding formula is great! you just mix with hot water and feed. You want it to be about the same temp as human babyfood. I use a measuring spoon bent to mimic the shape of a parents lower beak. They take what they need off the spoon. Is there someone at home all day? That would be one way you could ensure they won't go to nest again.