To me, this post sounds somewhat like you believe the manufacturer claims about Chemiclean, which IMO, are not how it works. That may not be what you think or mean, but I wouldn't want people to come away thinking Chemiclean removes sludge, as it claims, and that is how it works.
Chemiclean works within 48 hours oxidizing trapped organic sludge and promotes an ideal enzyme balance.
It is an antibiotic the kills cyanobacteria. It is not getting rid of cyano by "oxidizing trapped sludge" or altering an "enzyme balance", although I imagine folks at an LFS reading the label are readily convinced.
The use of particulate calcium carbonate is a way of reducing organics in the water.