Cat litter is just clay. Absorbent clay. Like what underlies half the state of Georgia. It's a triumph of marketing to convince people they
should spend money to buy a bag of dirt for the cat to dump in. Of
course a little science and engineering has to go into that marketing to make this dirt special -- so that it won't stink like regular dirt from the back yard. Clumping agents are mostly
bentonite, where the swelling of the bentonite when it gets wet causes the clump to form.
There are all sorts of tricks to remove the ammonia smell in addition to the citric acid I've already mentioned. Baking soda is not really effective in absorbing the odor of ammonia, because the product formed, ammonium carbonate or ammonium bicarbonate, easily decomposes to give off ammonia and
carbon dioxide. But almost any
amphoteric compound can be used if it will bind ammonium ion and give off hydrogen ions. If you have some sauerkraut juice, the lactic acid can bind up the ammonium ion, forming
ammonium lactate. Of course, then you may have the problem of the cat not wanting to use a litter box that smells like sauerkraut.
I would imagine that your "closed [pathogenic] system" is already host to
Toxoplasma gondii, since it is not that closed and the cats may be eating all sorts of wild rodents. Best thing to do there is to follow the
rules for how to minimize exposure, the most important of which is to
cook the eggs. The way you can tell if the chickens are having a problem with the toxoplasma level is if they start showing neurological signs. Which, come to think of it, might explain another
mystery that I haven't yet solved.
If it was me, I would forget composting cat poo and put it in a biochar burn. That'll take care of those nasty pathogens!