It does sound from what you say that the root cause of bingeing is emotional (to be honest, this is the most likely cause for most eating disorders???????)
About the 'hiding' which you say you've done all your life. Going now into amateur shrink mode (!!!!), again, can you see anything in your childhood and youth that might be associated with this? How strict were your parents? Did you feel 'denied' or 'ignored' etc etc. All the 'usual suspects' when it comes to why childhood experiences can haunt us all our lives? (I fear running out of money, as that was very predominant in my childhood, and scared me a lot. I also grew up 'knowing' I was ugly, as I was not beautiful like my mother)(etc etc!!!!!)
But maybe 'secret eating' is like 'secret drinking' - something we are 'ashamed' of as society regards both as self-indulgent. So we want to hide it and avoid the shame?
I'm glad the 'parent/child/adult' model resonated - the fact that I know about it is because it so struck my friend on the weight loss programme, so it does sound like it might be applicable in many cases.
I experience it too sometimes (since January and my DX into pre-D, I've been low cal and low carb, trying to force my Hb1AC down!!!), and always have. Like most women who are not 'born skinny' (grrrrr!!!!)(though, yes, they have their own issues and problems I know), I've never been able to eat all I want, in that if I did, I'd be the size of an elephant by now. Greed has always warred with vanity (and now as I get old, vanity is replaced by the desire not to have health complications from overeating!).
So I do get why and how 'the inner child' can suddenly get loose, and we go into 'hanged for a sheep as a lamb' etc etc....
I do think, too, that one of the toughest things is not when we have overeaten all our lives, and never tried to control our eating, but when we have tried repeatedly and 'failed'. It's like the bitter old joke - 'Giving up cigarettes is easy - I've done it loads of times'. Yes, exactly...
Then each 'failure', each 'falling off the food wagon', only reconfirms that we are 'helpless' and 'useless' and 'just can't do it'. Every failure reinforces failure itself.
It's interesting and I would suspect revealing that there seems to be no particular pattern, and no particular triggers. Yet triggers there must be one - no effect without a cause. 'Something' must set it off. It could be external and 'adventitious' of course. For example, if I see, say, a marked down sticky creamy calorific cake, or pud, in the supermarket, then I think 'Hey, a sign from God that I should buy it and eat it!'. That in itself can release the child. (It links, too, to my fear of running out of money, in that when I see a 'bargain' I think, hey, that will save me some money - even if it's something I shouldn't buy anyway, sigh)
One other thought that might, possibly, give you something of a handle. Would you say you go 'all or nothing' when it comes to the cakes etc? Do you have ANY limit when you are in binge mode? What actually stops you at the time? Is it because the cake has all gone, and the biscuits are gone, and the cereal is gone, etc etc - ie, there is nothing left to eat? Or is that you actually feel full by then (or sick, or both!). Or does something from the outside world 'interrupt' you - eg, a phone call, bedtime, etc.
Do you think it might help at all if you logged what you eat when you bingeing? I know 'the child' won't want to - it's a 'confession of shame' too for the 'parent' in you. (Did I really eat three chocolate cakes, four eclairs and three packets of biscuits'??!)
But if you wrote down, every night (assuming that's when you binge in secret??), just what you binged, could you then, the following night, resolve not to eat quite that much as the night before?
I'm not saying 'don't binge at all' - I'm saying, 'leave something'. Don't eat everything you want. Put just a little aside, every, every night. The purpose is to establish that you can control your impulse even just by a little - it's significant, i would say, psychologically and emotionally, even if the actual amount you don't eat is pretty trivial. Then, if that works, you could try and increase, every night, the amount you don't eat. (Obviously, you can't cheat by buying more carb food than you normally would, so there is a bit left over that way!)
You could also do this by carb counting - just tot up all the calories/carbs you have binged on. Again, you won't want to, but if you write it down, then do the same the next day, but deliberately set aside a couple of hundred calories' worth of cake, then you will have achieved 'management' to a degree - ie, you've gone into 'adult' mode. Only a bit, but it's the principle that counts. It's something to build on.
Finally, as we know, it's SO easy to think, the moment we 'lapse' that 'Oh hell, here we go, I give in, I've lost the battle so I might as well just stuff my face totally' etc etc. Which, even if you do do one night, does NOT mean you are 'doomed' to repeat that the next night.
One last thought for now - would a strategy of deferrment be helpful? That way, if your normal 'binge time' is, say 10 pm (as it is for my chum - it's when her early rising husband goes to bed, she has the house to herself, and he can't see her hit the cake....), if you deliberately defer it by, say, even fifteen minutes (and then eat whatever it was you were going to eat anyway), it, again, places you into 'adult' mode. You are now 'managing' the situation. You are deliberately saying, yes, I sahll eat that cake, but not for 15 minutes.
The idea is gradually to postpone, a little bit longer, a little bit longer and then, especially if it is bedtime, you find you are starting to 'time out' of eating ALL that food in the window remaing to you, so your overall intake is 'less' than it would otherwise have been.
I do think, I guess, that a draconian 'all or nothing' strategy is too high stake - gradualism seems more achievable, at lower pain to yourself, and with a greater chance of being long-term sustainable.