Pay attention to fiber? The research in support of that suggestion is execrable (pun intended).
I did try the 500-1000 calorie deficit for a number of months. My weight loss was on the order of 5-10 pounds, and I was hungry the entire time. And then I gained the weight back and more when I wasn't able to carry through. People simply do not lose large amounts of weight on small deficits. It's bizarre. According to the trash bin theory of body fat it should work. It doesn't. Almost like the trash bin theory is wrong...
The carb free living is sustainable and healthy. If you aren't going to read Taubes, then at least read Victor Steffansson. He's a bit more fun.