Biliary sludge is predominantly cholesterol, fatty acids, mucin with some calcium and salts. Biliary sludge despite its name will float in water. It sounds more like digestive waste which is deficient in bile; a small clay stool made up of flush products. As you said like most us get following a "standard" flush protocol.
I do hope other people let us know how they get on with the egg recipe.
Do you think you'll be following this protocol and do a series of regular flushes?