This might be a stupid question, but would it be helpful to deliberately eat excess kcals (when compared to your usual daily baseline), but in nutritious or mostly nutritious foods, before your period or in times of stress (and whatever situations trigger your binges)?
I understand that psychologically it's very different to slam down sugar (or alcohol in my case) and fats, because those are the things that our "lizard brains" are programmed to crave in times of stress and peril, but for me personally the best way to prevent a binge is to hork down a big portion of something high in fibre and nutrients even if I also add something to it that satiates the lizard brain. For example, a bean and pasta portion with a mountain of grated cheese and an extra splash of oil is probably still better for me and my caloric intake than skimping on the cheese and not feeling satiated enough to be able to stop the binge?
Also, what is the sensation(s) you mainly seek from a binge? If it's fullness, it might help to bargain with the desire to binge, f.e. "OK I'll give in but only after I have eaten two bananas", so the bananas increase satiety and might make the binge a bit less uncontrollable. If it's the feeling of relaxation or release from anxiety like it usually is for me, it might help to pay attention to the surroundings of the binge (I do this a lot); making the space pleasantly lit, wearing comfy clothes, possibly taking a shower so you feel refreshed before starting to eat? Sometimes I binge because I get too exhausted of being a "goody two shoes", so it also helps me to remind myself that there are no demon foods, moderation is possible even if it weren't possible for me right now in this moment.
I hope I didn't come across as rude or a know-it-all, just spitballing what kinds of things seem to work for me, copy or ignore as you feel fit. I know for sure that unadressed hunger and going too low on kcals is my number one binge trigger, so that's always something to keep in mind especially as your lifestyle is so active.