For somewhat smaller cats, Restaurant bins used to clear tables are $5 apiece and deep enough. I stack 2 and drill holes to make a sifter, which you could also do with the cement mixing tubs. Works well with pine horse bedding pellets as well.
Man I’m having this same problem currently with my big cat! I have to layer the floor under the box and the surrounding area too bcuz she will stick her butt out of the box and the shoot piss straight down or out even further. It’s really taking a toll on my anxiety!! I’m going to be working on making a box like yours this weekend but I think I need to go with an even bigger box 😰 love these kitties so much but, man they really grind the gears sometimes! Thanks for your video and your idea! Happy to know I’m not the only one going through it.