While I think the alternate day fasting is an awesome protocol on a lot of levels, there's no reason you couldn't modify it for your needs. If you ate 1000 calories one day and 2000 the next, you'd average out at 1500 calories a day, and probably lose the last bit you want to lose. It might take a little time, but you wouldn't make yourself crazy.
"Now I'm just another anonymous shut-in with an online shopping addiction." - Georgina Sparks.
"I puked like a hero for the rest of the night." - Anthony Bourdain, 2002.
"Brain: an apparatus with which we think that we think." - Ambrose Bierce