I feed the waste hay to my goats so I want to minimize bunny-berries in it. I have the corrugated plastic panels, and what I do is scrape the hay at an angle across the dropping boards- the poop stays in the "trough" and the hay falls down. I gather the hay and then do a second scraping to push the poo down. Mind you, when I clean out the area under the cages there is still a lot of hay mixed in, but not as much.
Another possibility is to sell composted bunny poo- that way the hay will have broken down as well.