I'm down with the stack. Use a square (I have a couple of 30-60-90 drafting squares and use them a lot) to set the stack up square and then clamp them together. I find binder clips from my office work well without denting the wood. If the wood does get dented by the clip, the CWF or whatever you use to fill the grain will fill that, too. Then set the sandpaper on a flat surface and only pull the edge of the fins across it. You want the vertical pressure to be toward the trailing side of the fins on the paper, so it offsets the tendency to rock forward in the direction of travel. Typically, for the root, this means holding the flat faces of the stack between thumb and middle finger, with index finger pressure on the leading edges toward the forward tip. Pull the stack toward the trailing edge, feeling the forces and keeping everything in balance to avoid rocking moment as much as possible. Only pull it, don't reverse the direction and the forces.
Works for me so far.