I've hand planed a bunch of things, with the sandpaper adhered to a very flat surface. You just swirl the part in figure eights, then opposite figure eights, and keep changing where you grasp the item every few revolutions. You can also alternate circular strokes while changing directions. If you are very attentive and consistent while doing this, you can achieve a relatively accurate cut of material, as long as you keep even pressure, and insure that your item stays perpendicular to the cutting surface, assuming a 90 degree cut. My father taught me to use lapping plates as a boy, a very flat piece of hardened steel with grooves cut into it. A polishing or cutting compound is slathered onto the plate and the parts are cut and polished as I described. When you described your situation and the modification to your base and the engineers involved, these things came to mind
We hand polish microsectioned circuit board coupons on the polisher at times, but it does get slippery with the polishing fluid, and we have been known to let one go flying across the room from time to time. Holding onto the base without the tank and top attached- we were worried about the vibration shattering the thin glass, seemed too risky. We also had all day to kill, since operations were shut down due to losing 480 v power in the shop...
