I used to use monitor boxes as well but monitors are now flat screen ones and the saddle wont fit in. So go down to your local supermarket and see what boxes they have.
A lot of horses dont know how to react on their own without their fellow herd members. This is why independence is so important. Owners often dont school or hack out on their own which is why the horse feels the need to go back to others in any different situtation for the feeling of security...