i have compost bins in rl and i always add charcoal and ash from my barbecues.
it improves the mulch.
so ash and charcoal should increase the quality of the resulting mulch based on there own quality.
but only once for, lets say every 20 produced mulch. so you cant "spam" ash and charcoal to increase mulch quality infinitly.
here a small wiki link on that topic:
https://en.wikipedia.org/wiki/Terra_preta
mrs. edit says:
manure could be a good addition for the compost bin.
produced by the chicken coop and from other animals, dropped on the ground.