EDIT: pardon the poos in the pic- I took the pics just now so I could post examples.
I am not sure if this will help you or not, but what I found is a coated wire bin from the “sink” section/ kitchen organization at our local grocery supercenter (Meijer).
In the NIC cube cage I attach it at the bottom with 2 zip ties- stuff it full of hay and flip it up and clip it closed with a metal clip. Most of the hay gets pulled out into the litterbox. When I change the box I always put a handful of hay on clean grid in the litterbox. I first had it set up to be an “open” top so I could just throw the hay in, but after 2 days Cotton obviously must have figured out she could jump in and poo on ALL the hay, so it was ALL hers (We are still having Cotton/Penny bonding poo/pee wars). So I had to change it so it could be flipped up and clipped “closed”.
The dog crate holder is zip tied in place- and the shelf above moves up to allow me to fill it but also acts as a “lid” to prevent any pooing in all the hay. The bins were about $5 and they hold a lot of hay. I stuff them full of the bulk bale hay and I give handfuls of Binky Bunny hay like meadow, oat into the litterboxes every other day or so. It seems to keep the buns interested in the hay.
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