Annie,
Just contemplating your idea and my first assumption would be that cutting them into strips (akin to making french fry shapes out of them) would increase the exposed surface area and that would be a positive advantage. However, the finer or smaller you cut up the pieces would begin to impose a finite limit to the advantage. As the pieces become smaller, they would fit together more tightly and reduce the advantage and thus start to trend the other direction because the shapes of the pieces and their sizes would then tend to "clump" together in a large mass which would be even less effective.
My opinion on this is this... If you cut them up in random sizes, some long and narrow and some wide and some in cubes, you might gain the best advantage as the individual pieces won't be able to pack into a large mass of uniform density. With the varied shapes and sizes, they will allow voids in between each piece which will be beneficial in the long run. There will be pockets where air bubbles can accumulate and break up the entire structure of the filter system into numerous mini filters.
So, if my theory on this is valid, I would cut the "scrubbies" and such into all different sizes and shapes and mix them all up in a bag in random order. In other words, I think your idea is on track and has merit, but I would take it further. Cut some pieces in round discs, some like long french fries, some like square brownies and so on. Then jumble them all up in your bag so they are placed randomly.
It is just a thought and if you admire it, give it a try and report back if it works well. Can't tell until you try it. Good luck!
Gordy