Thank you! I was beginning to think I'd never get a response! <sniff!>
Nope, no trays, just dropping boards with a slight slant. I don't know if you read the description or saw the rest of the pics, but I made scrapers out of the same corrugated material, and I scrape them each morning so I can feed the "waste hay" to our goats. I don't think you will find anything that is actually "self cleaning"- even when I just fed pellets, the droppings didn't all drop down. I guess it might be possible if you had a tremendous slant, but then you would need a ladder to access your top row! I don't use bedding except in nest boxes, and I raise Rex with very short fur... even so, that slight fuzz of fur will stop the droppings from rolling freely. I've had rabbits strictly as pets in the past and used cages with trays, and found that to be much more labor intensive- at least this way you are only dealing with dry waste. Scraping daily only takes a minute or two if that- it takes me far longer to feed them their hay. You could probably leave it longer with no problem, but I feel daily cleaning is a good management tool because you can check for loose stools, overall output, etc. If a rabbit goes off it's feed I will know within a day.
I would highly recommend building a wood frame to suspend your bottom cages from so you can place (screw) the dropping boards on top of the frame- at first I had my lower tier hung from the top cages by chain, but that meant we had to cut holes in the dropping boards and urine flowed down the chains. Thankfully we hadn't installed all of the panels before I discovered that problem!
Take a close look at the other pictures I posted, and if you are still unclear, I would be happy to take one of the end panels off so I can take a photo down the center of it. Oh- another thing I didn't mention in the original post- we put "step flashing" (galvanized metal used when installing a roof- ask at your hardware store) on any lumber that urine could flow onto or rabbits could spray.
Hope that helps!