KISS is a version of Atkins but linited to natural foods only.
Here is better explanation:

http://atkinsfanclub.freehosting.net/KISS/kissrules.htm

Here is a good Discussion

Actually i think that Atkins is more liberal then PP. Atkink is strict on carbs (not a big problem) but calories are not restricted. PP, on the other hand, says that calories are not counted, but if you look at sample menu - there are no more then 1100 calories a day.
They allow more carbs though.
I do Atkins Induction because i gained a little weight and decided to go on induction to loose it. I learned a lot of fundamental things from Atkins books, but never actually did induction. Had no need.
Your exersise seems ok. Maybe add some weight training twice a week or replace one of your aerobic workouts with lifting. Long cardio workouts have been known to send body into starvation mode as well, just like low calorie diet. I am no expert on this, but it may be worth considering.