not familiar with Twin Peak's diet.
Just substitute carbs with quality fats and protein.. it's pretty simple. Induce ketosis with little to no carbs for a few days, then after about a week of low carb eating, replenish glycogen stores with a carb up day or two... then go back to low carb until your desired fatloss is attained.. it works if you stick to it, and if you carb up once a week, you can maintain LBM quite easily.
most low carb diets are just variations of the others... in fact it takes experimentation to find out what is good for you. The conviction is the hardest part at first. Once you reach your desired weight/fatloss, I would recommend starting to slowly raise low GI carbs until you reach a proper MAINTAINABLE 45/35/20 macro breakdown to keep you lean, but balanced in terms of diet... and leaves the door open for building muscle.
Militant Underground Body Opus my Dan Duchaine is a good crash course in cycling carbs... and Gerard Dente's Macrobolic book is good once you decide to start to eat "normal" again.
just my opinion, but everyone is different.
