I think you have to decide where you are in this journey. For me to get my bingeing under control I had to firstly allow myself to feed both my physical and mental hunger. Denying either made me want to binge. Once I had gone a period of time without bingeing and felt like I didn't have to binge, I began working more on IE and trying to only feed my physical hunger. Denying my mental hunger meant getting bingeing urges that I just had to sit wih and feel uncomfortable with until it passed. I still do get the urges and sometimes I try to do something to distract myself, but mostly I just have to accept the feeling and know that it is just that part of my brain that is wired incorrectly. I can actually turn that negative into a positive by realizing I am trying to rewire it and decondition it. Every time I sit through that feeling and do not act, I know I am reinforcing a new behaviour and it gives me confidence to know I can get through the next time. This is not to say I never give in to mental hunger. I do sometimes. But when I do I am aware that because I am feeding mental hunger, there will be no shut off switch. So I do not count on satiety ques to tell me when to stop. I just try to stop. Like I might have some chocolate, and of course when I do I want more and more (the animal brain talking). Being aware of this helps me stop before it turns into a binge. Sometimes I am able to stop at just a little chocolate and sometimes I stop at alot. but I don't binge. The toughest part is not to feel guilty if I stop at alot rather than a little. But this is where the getting away from the "all or nothing" mentality comes in and instead of feeling like a failure for having too much, I remind myself that being able to have too much and not binge is actually a victory. I then put it behind me and try to improve and listen to my body more the next time. And sometimes the next time will be better, and sometimes it is not better. Overall though, I think I do do better with it all. It is like 2 steps forward and one back.
I think also you might be too hard on yourself. Maybe it is unrealistic for you to lose weight while breastfeeding. Maybe also the pressure you are putting on yourself to lose weight is actually causing some of this mental hunger. I think a big part of getting over some of the mental hunger for me was not tracking anything incuding what the scale said. I mean, how can someone honestly just relax at the end of the day when they have numbers floating around in there heads?
So I'm not sure if anything I've said helps. Obviously I am talking from my own experiences and what is helpful to one person doesn't necessarily apply to someone else. But it does sound like there are many positiive discoveries you have made. The key I think is to just keep trying things and staying positive and focus on the victories and build on that. We are all a work in progress. I am still progressing.