Hi,
Sorry I am checking the posts kind of late today.
If you have sawdust on the bottom of the cage itself, that’s probably a part of the problem. You want a clean cage bottom, not a wire bottom one btw, and only have litter in the litter boxes themselves. Bunnies don’t need sawdust, just smooth surfaces for flooring. Plastic bottom cages are fine, as well as low pile rugs or tiles. Anyway, you want to be careful to never use Pine or Cedar shavings. They cause long term illnesses in bunnies. Aspen shavings make a great litter, however. The paper-based brands such as Carefresh are good, as are pelleted pine, aspen, Yesterday’s News, etc.
It sounds like Buckley enjoys the brand of litter you’ve chosen if he’s hanging out in the litter pans. That’s a good sign. You want both pee and poos in there eventually. A good way to train him to confine the poos is to get them as soon as you see them elsewhere in the cage and toss them into the litter pan. This is frequent and tedious for you to do for a few days or even weeks, but he will learn that it’s the place they really belong. You can also put some hay in one end of the litter pan so he can munch and poop in there at the same time, which is sometimes why there are poos outside the pan.
One last possibility is that either pan is just too small, as many corner ones are for a growing bunny. If he’s getting around 4-5 lbs or more, change to a rectangular one for more room. My Sammy looks like she’s on a cruise ship now that I got her a really large pan, but she obviously loves it and uses it even better than she used to.