That effective and economical system would probably consist of the classic anaerobic lagoon and spray irrigation system that most of the pig farms in the western US are using.
We developed an effective product that reliably supports a change from anaerobic rot to aerobic decomposition. Bonus: is very economical and inexpensive.
The product is on the market in Europe since over 20 years, however so far has not been introduced in the US, could be imported without problems though.
Calcium Carbonate soley acts as a neutral carrier substance, it is treated in a proprietary manner which causes the desired effect.