Re: not what you want to hear, but...
The good news is I am at least pleased to see you have an open mind. I think that is 90% of the battle. It's a great philosophy to ALWAYS keep an open mind, in my view.
The bad news is that I have seen lots of people try to lose weight by fasting and fail miserably. Some of them said they too have said that they believed god wanted them to fast, but the cycle kept repeating. I am open to debate, but as things stand I really think that the advice given in the FAQ is correct, and that a water fast cannot resolve this issue as it will simply be a form of purging in a binge / purge pattern.
I did look through a few other of your older posts and blogs and I notice in your blog "why does this happen" you had problems with kidney stones and had to break your fast. Fasting does place hard demands on the kidneys. And although I am glad to see that outwardly you are in good spirits, I am sure that it is not very nice to feel a sense of failure after 4 years of attempting to fast and failing, sometimes with health problems, only to hope that the next time you might succeed. It can't be good for your self esteem either.
I am sure there are others here in this forum who will give you support and make suggestions. Because I have not had the problem of an eating disorder as such I cannot speak from experience, but I did come across this post a few days ago which may have useful video and link content (though I am not sure about the presentation!).
My personal view is sort out the issues surrounding the eating disorder first, then consider fasting. You may then find you don't have to or don't want to! 
Oh and it would be really great to see you as a success story here one day, however you do it!