I personally would confine him to the bathroom (or any non carpeted room) when you are not home to supervise him. He can romp and play when you are there. If you cacth him in the act of innappropriate pee,or pooing , then you can correct him IN the act. (although with cats, most of them are higly "indifferent, of scolding or correcting)... But while you are away, I'd put him confined to a room, with no carpet, and the GIANT box you plan on having. Then when you are home, let him out, and give him a treat if he pooed or peed in that giant box. May work , May not...but at least your having less clean up everywhere, and dont have to do a "hunt" of where stan let loose.
Edit> (ONLY posting this to explain that some people do go to great lentghs to stop kitty from innapropriate potty issues. I am not condoning nor suggesting below action)
my friend once had a kitty that liked the laundry basket and one paticular corner of her bedroom closet to potty in. She tried everything you have...and then one day an idea hit. It sounds so cruel, and i wouldnt do it, but it did work.
She put extra sticky duct tape , tape side up, in the NO NO spots. ....after having duct tape stuck to his feet, and then everything else on his body because he was trying to get it off....he learned to stay away from those spots. ( left the tape on him for a day or so , to let him be good and annoyed)..then she got it off with goo gone. Then he got a bath because of the goo gone. needless to say..he was one UNHAPPY kitty at the end of it all. She only had to do this three times. He has never went in her closet or basket again. he wont even go IN the closet, or CLIMB INTO a basket now.