You could try giving them things to do like hanging greens up for them to peck at. My daughter discovered chicks go bananas over grass seed heads so that would be another activity that might wear your trouble maker out. A clump of dirt and grass is also a good boredom buster, giving them something to pick and scratch at, and I've found they like sprays of millet that you'd give a budgie/cockatiel.
On sunny days you could try putting them out in a little pen as well to start getting them used to the outside world. They'll let you know if they are getting cold by peeping miserably, but they are often more hardy than you'd expect. I think your baby is just at the stage where it needs more to think about and do, and with only one buddy who doesn't sound like it shares this ones enthusiasm for play, it's just looking for ways to have some fun.