The simplest thing would be to deposit liquids in one container and solids in another at time of use, to reduce the 'slop effect'. Bundle up the solids in sturdy bags (contractor bags are good) and fasten them with a cable tie (not a twist tie) when when the weight gets to be 'about right'. Don't load up a big bag to capacity -- think about having to empty it.

Forget the chlorine, that's really nothing but 'eyewash' (to make people feel they're doing something). A little chlorine isn't going to decontaminate twenty pounds of feces.

If you have access to water (doesn't have to be drinking quality -- used wash or bath water is fine), dilute the fresh urine about 1:10 and sling it out over your lawn or under your ornamentals, it's good fertilizer as long as it's diluted. The soil microbes should make short work of it, esp in warm weather. Try not to store it, or it turns to ammonia and really stinks. (Try to deposit all toilet paper with the feces, rather than dropping it into the urine.)

Alternatives to raw sawdust is stove pellets, or 'bedding pellets' from a feed store, easily stored in their own tough plastic bags, and pretty cheap ($3.50-$5/bag).

Sue