Yeah, also have to make sure the big 'pixels' only move in 1/84 steps. This sort of rules out physics engines because they will move everything on a granular level, if you move things yourself you can round to the nearest 'pixel'. In last year's game I stored the position at a precise level, but when it came to actually moving the object I rounded. Then you can get smooth acceleration that still snaps to pixels, rather than speed being clamped to 1, 2, 4, 8 pixels per frame.
Having written that you could use physics, just hide the 'real' object and show an object which takes the real object's position and rounds it before displaying.