Sounds like you've been doing some worthwhile research and coming up with fine conclusions for yourself. :) Keep it up!!! be your own expert!!! :)
Multiple Liver Flushes are definitely called for, and the fasts themselves can cleanse the liver too, so that should help with dealing with the estrogen released by burning fat. The carrot,apple,beet,parsley,ginger drink is especially good to the liver. :) And you can safely take herbs like Milk Thistle while fasting, to make the fast even more of a liver detox.
Apple cider vinegar is both potassium rich AND good for softening liver and gallbladder stones, which is why I add it to The Master Cleanser drink.