Speaking from personal experience, it is very difficult to reach higher maintenance levels without eating any fruits or starchy veggies (corn, green peas, butterbeans). You simply can't do it from nuts, cheeses, and green leafy veggies, at least not without spending your whole day eating and being miserably overstuffed. Consider the following:

8 c raw broccoli flowerets (12g)
1 head cauliflower (15g)
1/2 head cabbage (15g)
16 oz raw brussels sprouts (20g)

Now, my personal maintenance level seems to be somewhere around 75g carbs, so I could eat ALL of those vegetables in ONE DAY and STILL have ~15g left over for cheese, peanuts, dressings, eggs, etc. I really like veggies, and I generally have a big appetite, but even I couldn't eat much more than half of that in a single day -- it gets to be a simple problem of food volume. It sounds easier to eat, say, 20g of peanut butter, which is only half a cup, but it's so filling (and high-calorie) that you still won't want to eat anything else. Likewise, cottage cheese is 4-5g per half cup, but I have a hard time with eating more than a cup or so a day. So yes, it helps immensely if you can eat some starchy veggies, or some oatmeal, or some lower-GI fruits.

I know you say these are major binge-inducers for you, and I understand how that's a scary thing, but "fruit" and "grains" are awfully broad categories. Berries and melon may not do the same thing to your blood sugar as bananas; likewise, steel-cut oatmeal may not activate wheat sensitivities like pasta or breads will. With some experimentation, perhaps you could find a few foods that work for you? As for the beans and potatoes, I don't eat these myself, and see no problem with never eating them again.