Hi -- this is my way of keeping my housebunns--I know it's only one of many ways--I have a plastic underbed storage box with 6 inch sides. I put a thickish layer of newspaper or other material on the bottom. Then I put a "sink protector" (which one puts at the bottom of a kitchen sink to keep glasses etc. from breaking--it has little risers and holes in the plastic for drainage). Then I put a layer of "pet screen" (a little heavier than regular screen, so that cats/dogs don't scratch holes in the fiberglass screen door-- I thought bunns might chew at the edges but they never have). On top of the screen, I put their hay.
My three bunnies' poop rolls around, the pee mostly soaks into the botttom layer, and more hay stays fresh for them to lounge on, or eat. I've been doing this for years, and although there's an initial setup expense, everything lasts long years. I clean with undiluted vinegar, soaking as necessary. The white feet stay white.
I question your judgement that your bunn is "lazy". Cecotrophs are usually taken from the anus, but sometimes they aren't and they get stepped on. That's gooey. But the fecal pellets shouldnt be gooey. Im wondering if they are pee-soaked. In that case, the living quarters involving the latrine can be at fault and should be changed! Bunns can get sick from reingesting fecal messes, either their own or a companions'.
On pinterest and other foto sites
there are nifty ideas for making
pee screens for litter boxes. Ill chase them down for you if you're
interested. Please let me know. I've picked up many pointers myself from this forum!