I think what many people don't understand on this thread is that Binge Eating Disorder (BED) IS AN EATING DISORDER, especially when it is accompanied by some sort of compensation (e.g. fasting, vomiting, running more than your training plan calls for to "make up" for the binge).
Binging, especially at night, affects sleep, which in turn affects running. It also can cause constipation or diarrhea, neither of which is good if you have a run the next day.
The first step in getting better is eliminating "compensatory behaviors." The best thing you can do after a binge is eat exactly what you would normally eat. After a binge in the range of 3000 calories (which I have routinely had in the past , as many times as 2-3 times a week), I have found that the best way to get on track was to eat normally the next day, not to eat less.
You also may have another problem that your binge eating is a coping mechanism for. My BED developed as a result of depression from Seasonal Affective Disorder. The best way to figure out what you "triggers" are is to keep a journal of emotions, times of day, and circumstances surrounding both binges and times where you are able to avoid a binge.
I hope that helps, BED, like any eating disorder, is tough, I am only just beginning to get over my own problems which have gone on for years.
If you find someone else who has gone through this, absolutely talk to them about it, it is incredibly helpful to do so.