Hey Tom.
I have a Flemish Giant Rabbit, and my compost has never been happier. She free-ranges in our kitchen, and we let her out to explore and hang out in the rest of the apartment when we're home (she's still a rabbit, and loves to nibble furniture, shag carpeting, wires, spider plants and even leaves off of our avocado
trees).
I love the rabbit manure because it can be applied directly. If you can get a sifter that lets the droppings through but retains the bedding, you could separate them out to some extent. We use a wadded paper bedding, new paper processed from the pulp paper waste stream, that the worms in my garden just eat up.
Incidentally, the high-carbon nature of the bedding portion can be a great benefit when adding high-nitrogen kitchen scraps, and if it lacks the nitrogen to get composting, all you need do is
pee on it.
I have a ground-connected composter in the backyard of the flat I rent, along with a nice, though shady,
raised bed, but I have thought about how I would deal with my rabbit's litter in close-quarters short of throwing it out, and I think I would use the largest drum-composter, one of those that are mounted on a frame to allow it to turn easily, that I could fit in the space available, and I would make the hottest compost there as I could, perhaps keeping sealed buckets of overflow scraps to add at need, as the one thing you won't be short of is
carbon.
To this I would add at least one planter or large pot that would primarily act as a vermiculture bin, with perhaps squash, courgette, or other heavy-feeding fruit-producer living in it. The resultant worm castings could be harvested at need, to make room for the next finished hot compost contribution.
But this is highly dependent on space, and whether or not you can get a composting worm there.
I think the other obvious choice is to see if bokashi will work in your case.
But keep us updated, and good luck.
-CK
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein