I've tried the AD diet with much success a couple different times. You can see my progress pics on this site, just search for them. There is an easy answer for your question. Even though Dr. D says you can have any protein or fat while staying low carb, this doesn't mean you have to.
Take a look at your food choices. Cheese, suasage, pork rinds? Come on dude, you know better than this! Chicken breast, turkey, egg whites (with some whole eggs mixed in), lean steak and beef, olive oil, flax oil, EFA oil, almonds and natty peanut butter(watch carbs). Stick with these during the week then enjoy your weekends.
If you really want to get lean, keep your weekend load relativly clean while still getting enough to replentish glycogen stores.