I feed mine in crates, on a puppy pad. (Used to use newspapers, but they stick to the meat) I used to put the paper straight on the floor, but they would hide things they didn't like behind the sofa cushions.... One time Bambi hid a piece of spleen (apparently it tastes very yucky!) in the laundry basket, where it remained hidden for several days......So now it is crates only lol.
Yummy things like pieces of chicken and ribs etc don't last long enough to be dragged around the house, they are immediately eaten, on the spot. So since you won't be feeding offal, I don't think you will have a problem. You have to supervise them eating bones anyway, just tell him to stay on the pad/towel or whatever you designate as his eating area, and put the bone back on if he tries to take it away. They soon associate the towel etc with yummy treats and learn to stay on it.