Hi there AnimalBrain, sorry to hear you're struggling with this. If it helps, it's probably much more common than you realise.
I have a success story of sorts - potted version is... I struggled along for a few years in a binge-restrict cycle after a post-baby crash-diet. I would eat many thousands of calories over what I needed one day, and try to make up for it the next through severe restriction, usually unsuccessfully. I was unwell, depressed and worried I might be permanently damaging my health. I tried everything, read every book about BED / bulimia there is. I saw some small improvements but nothing significant or permanent.
The big change came for me when I started a CBT course for binge eating. The principles behind CBT for BED are in line with the Fairburn book that lots on here have recommended.
The key principles are eating regularly, eating enough, and problem solving, i.e. identifying urges to binge and solutions to these before they happen. My one caveat is that I think that approach can only help if one has truly put aside the goal of weight loss. It's not a diet plan and I think many people with BED understandably focus on the quick fix of undoing the damage, rather than on long-term health.
While I've had a huge improvement in terms of frequency and severity of binges, I still have periods where I need to remind myself of some of the things I've learnt, but I'd say my eating is closer to being that of a 'normal person' now, if such a thing exists! It's a huge relief not to be stuck in that cycle any more, I can't believe how much of my time and energy it was taking up. And money too, as my weight being stable means I'm not having to constantly buy new clothes!
For me, having some accountability was also a huge help, as I'm (unfortunately) one of those people that craves external validation! It would be great to get the thread started up again - I'm sure there are lots of sufferers floating around who could do with some support. Do you think that would help you?