Dr Atkins recommended a fat fast where you restrict your calories to around 1000 and almost all those calories are from fat. The purpose is to induce ketosis not particularly to lose weight-and is meant to be done a very short period of time.
He never advocated an egg fast or a meat fast...those are made up by fad dieters-crash diets with no basis in nutrition or science. Crash away if you want but don't make yourself sick over a 5-7 lb change-you want to be a lovely happy bride not a sickly,shaky waif.