The fatty material that floats may be bile or the olive oil.
I only say one thing: eat lecithin
Everyone should eat it in masses, it works like soap on a greasy plate, it works on the fat that you ingest and in the liver. It emulsifies fat, it can even clean fatty deposits in arteries throughout the body. People have reported weight loss when they start to eat lecitin since it helps the liver to burn all that fats instead of storing it.
Lecitin granules +3-5 tbl spoons daily. Doctors in Germany tell their patients to eat lecitin for the gallbladder stones instead of surgery.
Avoid fats? The liver NEEDS FAT! Stone formation is due to stagnant bile and fat accumulations because the bile have been sitting there too long. Each time you eat fats the liver pumps out bile and "flushes" itself, the Liver Flush
does the same thing but will all that oil and lemon juice the gallbladder contracts heavily and the liver must pump out enough bile to match all that fat in the oil. So all the debris in there gets out at the same time.
The liver must be working and pumping all the time, you HAVE to eat fat. Skipping breakfast is a big no no - there is a logical reason behind this, you have to break-the-fast after a long night and grease up that spongy friend in there.
I dont know if you should exlude meat, the liver needs amino acids to have a functioning phase 2 detoxification.