I have BED. The binge you describe in your OP I'd painfully familiar to me. I promise you I've been there and I thought I'd never escape it, but I think I might have only gone and bloody done it?
I strongly, strongly suggest that you do NOT follow any kind of 'plan', join any Slimming Club or cut out any food groups.
I stopped binging only when I accepted that I could never diet again. I read a couple of books on intuitive eating and it made sense. It was only when I gave myself unconditional permission to eat whatever I liked that the urge to binge stopped.
I think it was the scarcity mindset. Initially I pooh poohed it, thinking that my body would 'intuitively' want wall to wall doughnuts and pizza. But I gave it a go as, frankly, I had nothing left to fucking lose. Weirdly, the first thing I wanted to eat was peanut butter on toast with raspberries. I had a salad on that first day, and then we ordered dominoes. I had three slices and then just...stopped. It was bizarre, like a switch had flipped. I put the rest in the fridge and shared it with my DP for lunch the next day. Like I knew I COULD have it, so that panicky 'eat it, eat it before it gets taken away' disappeared. This doesn't happen every day btw. I had pizza two days ago and ate 5 slices because I guess I was hungrier that day? And it was fine.
I've not binged for months. I always have my trigger foods in the house now. I eat them, I enjoy them. In the beginning I definitely ate past the point of comfortable fullness from time to time, but because my satiety signals were out of whack and I was still working them out, not because I was out of control. It wasn't that frenzied binge feeling that I'm guessing you understand.
I still get cravings and I give in to them. This evening I helped myself to an extra piece of almond chocolate because I fancied it and it was lovely. But I also crave vegetables and fish and apples. I feel like I'm eating like a normal now. I never, ever thought I'd be able to. I'd say prepare to spend a few weeks thinking about food ALL THE BLOODY TIME. And then, the food noise just goes.
Now I just make sure my meals have fibre, carbs, protein and fat in them in some way. My only real food rule, other than eating when I'm hungry, is 30+ plants a week, which doesn't feel like a restriction as its adding things in rather than taking them away. I enjoy the game-ification of it. Other than that, no rules. I eat three meals a day and sometimes a snack. I'll have cake if I go for coffee with my mates. I might eat a biscuits in work as long as I decide I want the biscuit but I can leave them if I decide they don't tickle my fancy at the moment. It's liberating.
Also, although IE is specifically not about weight loss and any good IE nutritionist goes to great pains to say that they don't know what will happen to your weight if you follow this approach, I've lost about a stone and it's still going down. It's incredibly slow and at some point I accept it will stop, but it's better than before. I, like you, was well into an obese BMI so I guess it was a natural side effect.
Point is, diets make you binge.