I think there are a few things going on here. First of all I believe that focusing on food when kids are young teaches them to focus on food as adults. My parents always made me finish everything on my plate and most times would tell me to eat "just this little bit more, it isn't enough to save." I grew up to be an over eater. My point is just that habits are being established and that may be what the Doc was talking about with control/future Anorexia.
I go through this in spurts with my kids ages 2,4,6. I believe that many times the gagging etc, is a case of mind-over-matter and not a sensitive gag reflex or texture issue. Man, if she can eat vienna sausages, she can eat anything! That said, the food thing can be her way of getting your attention. You are a single parent and working. I seems like dinner is the only time you guys have to sit and talk and it is too bad that it is wasted on discussions about food. Maybe you guys need to work on discussing things you have in common, or weekend plans, or ask how your daughter's day went. If she is distracted by positive attention, she may not be inclined to complain as much about the food.
The other thing is that your daughter needs to know that you are the Mother. Make her have "try-it-bites" of all the foods you make for yourself. I have found reverse psychology works really well especially in stages where they have a natural instinct to contradict you. After you have tolerated her faces and complaining for a while on the tryitbites, before you give her a bite of something, tell her she can only have a little bit, because she won't like it anyway and you like it so much you don't want to give very much away. She may just decide she likes it and wants some more...or not! At least it is worth a try.
In the meantime you can give her Cheese Quesadillas, but insist that there is chicken in there once in a while or that she dip it in salsa (vitamin c) or If she has boiled eggs, she has to eat a piece of wheat toast with it. Come to a compromise, where she still has a lot of control, but you are ultimately in control of her nutrition.
Another idea comes from a really cute book called "Bread and Jam for Francis." The little girl turns her nose up at everything that is put in front of her except bread and jam. The Mother decides that bread and jam is all she will get to eat from now on and serves only that to her for every meal. Then the other family members talk about how delicious their food is but that Francis can't have any. You could just make quesadillas for her every night and make real food for yourself. Instead of making them in a pan (if that's what you do) you can just stick the cheese on the tortilla and microwave it (saves time for you). Then make yourself a meal with balanced nutrition and a lot of taste! Do this every night for a while. Even when you go out to a restaurant, order her a plain cheese quesadilla and get something else that you know she likes. Then it will be apparent who is in control.
I like the idea of mandated nutrition drinks and if she doesn't like those, tell her that she has to drink them until she becomes a responsible eater. Also from the foods you listed that she will eat, I would be concerned about her bowel movements. There is a lot of cheese in there which can cause constipation. Constipation can then cause nausea and gagging which just compounds the eating issues. Try getting some fiber in her diet either through pear juice, citrucel, or by using whole wheat tortillas for the quesadillas. Be gentle, be loving, and be in charge!