Using a box grater
After a while, it ocurred to me it would be better if I could put a little more pressure on the squash pieces, and after staring at the setup for a minute I laid the grater down on its side, since it's always easier to press down:
This arrangement turned out to be so efficient (I could press down, now suddenly the handle of the thing was actually useful since it was positioned opposite the tugging force of grating), that it occurred to me this is probably how they are SUPPOSED to be used.
Have I really been operating a box grater incorrectly for 30 years?????