RE: Cutting down APC props
Aw hell, cut away!
I have cut down many props for a variety of reasons. Different brands too - wood, composite (Although I wouldn't cut a carbon fiber prop, but standard run of the mill props, sure)
And just for the record... No, I DON'T balance them before OR after. Of course, I am very careful to remove the same length off of each end.
But I will also add that I would NOT do this for a prop that will be used for extreme-speeds (Like over 12,000 RPM)