I have not tried charcoal as a filter… With perlite also having a massive surface area, and it being white, I just stopped experimenting with cloth, paper filters, and foam when I could “see” what I was filtering… To reuse, we simply shake it out with a fine sieve, and put a blow torch to it to incinerate any fines that are caught in to nooks and crannies… it’s also so cheap that you can toss the used batch into your compost pile and start fresh.
I don’t know if it’s the ultimate particulate filter, but I really like it. I don’t see a need to switch.
As for depth and cross section… I just wing it. I treat it like charcoal in that I “eyeball” the size of the grains, and imagine the breathability within my filter box.
Caveat: you must use the course grade perlite and sift it for fines.