It took you a long time to gain the weight, so please be patient. I know thats easier said than done. ;-)
I would first get the thyroid checked and out of the way. If it is your thyroid then the fat fast won't work well enough and you will get discouraged.
If anything I would look more towards a yeast problem first. I believe Atkins says to rule that out before trying the fat fast.

Good luck and I hope all is well healthwise and beyond.