Don't Know What I Want...

I didn't realize that you were actually eating a lot and then purging rather than restricting.
I am recovering from restrictive anorexia. I am not sure how the binge and purge cycle effects things. I do know though that I am uncomfortable digestive wise eating my dietician given diet which is significantly more than I had been eating. Like you, I am uncomfortable being full. Although I have some normal appetite now (it had disappeared for a while), I don't have normal fullness. If I eat too much, which sometimes is part of the recommended plan, I feel sick rather than normal fullness. If your digestive system isn't used to working much, it doesn't magically turn back to normal when you get normal food. I get lots of gas, bloating, and constipation. They assure me that this is normal. I have read that these symptoms can get very severe and health threatening if you make too drastic of changes, but you might want to check with a dietician or doctor to see how this would apply to you.
One thing that you could try to get used to not binging and having food in your stomach for a while is to divide your food into small portions. You could eat one portion and weight for a certain amount of time before reaching for the next portion. As far as cooking, you could cook a time consuming, healthy, lower calorie item like a soup with lots of differnt vegtables.
As far as your weight, it is a sign of health to have a period. If you don't want it and don't want to have children any time soon, you can get deprova shots. I don't know if you need to be 120 pounds. Certainly that is not overweight. I am 5'5' and my dietican tells me that I would be healthy at 115-120 pounds as long as I am eating healthy (enough nutrients). Since you are 5'2'', you probably can be healthy at 100-105 pounds if you are maintaining that eating a healthy diet. I am guessing that eating disorder centers want you to be heavier than a minimal healthy weight so that you won't relapse as easily.