I don’t think the area they are in is predator proof, so cardboard boxes wouldn’t do. Though a small wire cage like this is also insufficient... As much as I dislike having chickens in the house, some large moving boxes with a wire screen on top (we use part of an xpen) is really the easiest solution to brooding. Or a coop with a heating pad, but we don’t have electricity out by the coop. I would brood in the house until feathered, keeping them on the cool side to speed things up, and then put them in the coop asap...Most likely they are pecking them off the heating pad because of space.
Can you get several large boxes and tape them together to make a larger area for them?