For general tidying up, however, I think it works well to be all over the map. One of the problems people have with focusing on one spot is restlessness. Focus requires mental attention and physical discipline. When the physical part is difficult, moving around is the solution. Hence, the walkabout tidy-up.
Instead of making a pile of stuff that goes to other rooms, just take the things there as you find them. When you get to the next room, see what you can tidy while you’re in there. Move from room to room as it suits you. Staying in motion can do wonders to keep you on task. In fact, it’s important not to sit down because you don’t want to start reading that magazine you just picked up (no reading while standing!).
Walking around also gets your blood moving and helps energize you. Sprinting from room to room isn’t necessary, but if it makes the job more appealing, try it! It’s always worthwhile to try a technique you haven’t tried before. It could work, or it could give you new insight into why you do things your way.