Sure, why not go ahead with your nice, clean break? It sounds like you know how to proceed, and as long as you don't do anything crazy (like eating an Egg McMuffin!), a good, cleansing diet will do you just fine.
You absolutely should be parasite free before flushing your liver. Liver is a very common place for the little devils to hang out, and no sense flushing a liver with live parasites! Once you've taken care of that, I absolutely agree that flushing your liver clean (you need to wait two weeks between flushes) can do miracles for your skin, as it certainly did for mine! Good news for you -- the long fast has been a good pre-cleanse for your liver, the reason I believe it only took me 5-6 flushes before I passed the Mother Lode -- 30-40 beautiful jade green stones the size of small prunes! Since that flush I have had ZERO skin troubles (after years of "adult acne" and "rosacea"). A true miracle in my life!
Liver Flush is controversial among health pros. Some swear by them, others don't like them. I can only tell you my personal experience -- Liver Flushing is an amazing, cheap, very effective cleanse of a much overworked organ. Our skin is only as clean as the blood feeding it, and of course the liver filters every drop of blood, all day long. Clean up the liver... all sorts of wonderful things happen!
Be aware that you can continue to experience detoxing symptoms as you break, if you were already in the middle of a crisis. Stick to the cleansing diet, and continue to drink lots of water. Keep your colon clean, and you'll get through it!