I haven't tried the actually fat fast, but I have found that a super high fat diet works wonders for me. I lost most of the 40 pounds I dropped by eating either twice a day (as much bacon as I wanted around 1 pm, which was usually around six or seven slices and 2 fatty burger patties with 2 slices of cheddar cheese around 7 pm) or once a day (2 burgers, 2 slices of cheese, 4 or so slices of bacon at 6 or 7 pm). This worked great for me, for around five months, until I started to feel like yakking at the sight of a burger.
I am not so keen on calorie restriction, though. Also, if I was gonna do the fat fast, I think I'd see what happened with the whole 1,000 as one evening meal. 200 cals at a time sounds kinda torturous to me.