Since you think cold turkey (not the food) would appeal to you, why not try intermittent fasting. You can google it. Just eat say during 6 hours each day, or eat every other day. Your stomach shrinks and you can really savour what you do eat. I find it's helpful for controlling obsessive food thinking and also resetting your appetite. After not eating 24h, a salad or old frozen burrito from the fridge like I'm having now tastes as good as dessert.

About the vegan or other restrictions, I can't comment. I just focus on quantity, and if you're binge eating I guess that part is relevant to you too.

>Basically at the moment I cannot come up with a grocery list...I just can't decide what to buy that I can eat, that won't cost too much and will also not cause me to binge.

You could pare it down to essentials that are the cheapest for value - like yellow pea and bean dishes from scratch, with seasonal veggies or frozen spinach with olive oil on the side. All you need.

An easy starter recipe (happens to be vegan):

http://electronworks.com/recipes/Rasam.html

I use 1/3 the tomato sauce or just triple everything else and use a full can.