Pit or vault toilets in campgrounds are not as bad as what your are describing so I would suspect there is some problem beyond the waste material. Regardless you might ask someone at a campground with these facilities what they throw down as it is definitely not bleach.
Filling the waste tank completely and putting in one of the enzyme products designed for septic tanks is another thought along the lines of it can't hurt and might help. Let it sit for a day or more and then empty the tank.
Beachhead makes a disinfectant that is used in food processing plants and hospitals and morgues or anywhere there is stainless steel equipment that needs to be disinfected and bleach is not an option.
