The "out of registration" cut is do to a tracking issue. CarveWright recommends doing the cut outs as a single pass using the 3/16" cutting bit but a lot of carvers shy away from doing single pass cuts for fear of breaking the cutting bit. Especially if cutting the full thickness of the board.
On yours it sounds like you are cutting out a pattern carve. You can cut down on some of the carve time with a pierced carve by making the outer pierce area smaller (closer to the pattern). When I am setting up cutouts for a patterned carve I use the feather tool around the pattern to remove the material around the pattern and then do a single pass cut out.