i think the guys are correct that there is likely more to the binge eating and extreme weight carriage which is buried deeper down. this is not only about food and nutrition, but rather your emotional/psychological relationship with food, consumption, pleasure, happiness, and survival.
the diet you are proposing may help in the short term, but i don't advise it. ask any medical professional and they will indicate some serious potential side effects (e.g. ketosis for one, and complications for liver and kidney function) if you try to sustain this diet over several weeks/months.
studies show that fad diets don't work. they tend to rebound and in a worse way. this rebound then compounds the underlying psycho-social issues and if you gain more weight than you initially lost, you're going to feel worse than before, and the cycle will continue.
the only way to lose weight is through a gradual reduction of calories, a proportional increase in cardio-vascular exercise, and eating a balanced diet of whole foods (which are not processed or contain a lot of saturated fats). the counselling can help uncover the unconscious relationship you have with food, and you may discover that this awareness will have an impact on your consumption habits.
i wish you the best of luck!