Based on measurements, the Cuddy Lite height does seem problematic. Fortunately there is some flex in the lid, so it does just fit. The aluminum bench cover rubs on the lid, so we added a towel on top, but even with that and a pad under the toilet to prevent shifting and scuffing, the bench lid closes.
We're the opposite of Mr. and Mrs. Chadx, and have yet to uses the toilet for liquids, which go on local vegetation. We do prefer it to cat holes for solids, even in 20s F weather. The plastic warms up pretty quick. We include the toilet paper for convenience, and remove the bag daily and keep it with other bagged trash in a collapsible bucket in a Roam box mounted on the back of the camper. With regular trash stops, no issues with odor, so I haven't had to dedicate a dry bag to storage, although that's a good suggestion.
As
@Chadx notes, small "composting" toilets do not do any composting. And you wouldn't want to try to compost solids anyway, without the industrial scale that sludge is composted at. Even if you could get it hot enough for long enough to kill pathogens, the solids still contain heavy metals and toxic chemicals that come from eating at the top of the food chain. Best to just put in a landfill like disposable baby diapers.
Here are a few shots of the Cuddy Lite to demonstrate the fit. It does need to be taken out of the shower enclosure to have the geometry right for use. In campsites with traffic or cold/wet weather, we put it in the outdoor shower enclosure. When we have an area to ourselves, we enjoy a "loo with a view," something I learned to appreciate with groover placement on river trips.
(For reference, I'm on the Tremor forum as @SuperGuck.)
