I also don't believe in Atkins (especially, well, the meat part). I've lost a substantial amount of weight by cutting out "empty" carbs. No flour, no sugar, no fake food (ESPECIALLY NO FAKE FATS, they are usually just replaced with bad carbs), except I do use a sweetener like Splenda.
Mine is actually a pretty high fat diet (think olives, avocado, real cream, cheese, all the nuts you want pretty much, because you feel so satisfied with so much less food, and chew, chew, chew), a cup of clear hot broth before at least two meals, and really really small portions. A relative of mine had gastric bypass surgery, and her post-surgical diet for some weeks was broth and teensy portions. I thought, why have the surgery if the diet you have to follow anyway works? (And it does.) Anyway, it worked for me.
your diet is similar to mine.. (lotsa fat.. cheese is my downfall).. what do you have for broth? do you make up a veggie type?