I can see it's an old thread but maybe someone someday will find it helpful...
@graphicminion: I'm not an expert but I have asperger's and I was a very picky eater (by the way, I'm still a very picky eater to be honest). When I was a child I didn't eat so many kind of things than your daughter, so I think you wouldn't be so worried. I was a meat and cheese eater, but first and last I ate the most 5 kind of things and those things must have been in the proper form otherwise I didn't even looked at it.
When I was a teen, my mother tried to take me to the market as many times as she could. These ''market days'' were not about buying stuff but about being together. We just walked between the rows of products and my mother told me stories about the veggies and fruits I'd never tasted before. These stories were mostly funny but told me how that particular veggie or fruit were used by one of my relative. I think my mom told me these "tales" because she wanted me to know better our family and they were nice memories for her, but for me, they were the credit for a whole new cuisine after growing up.
It means that as a child I didn't eat most of the things she talked about in the market, but later, when I decided what to eat, I was much more confident trying those things because of my mom's stories.
I don't know your daughter but I know myself and some other aspies. For most of us as a child, lunch and dinner time were always a little bit tense partly because we did not know what we were asked/forced to eat again we didn't want to, partly because we never want to make anyone disappointed we love and we did know that our eating choices are not fully accepted by the ones around us. That's why those market days were so useful for me. Those were about the stories without any stress on swallowing new things. Those days gave me infos without forcing me to do anything I couldn't do at that time.
In most cases we need looooooooong time to change. If you don't stress yourself but teach her without forcing her to use the knowledge immediately everything could be much easier for both of you. We are very sensitive to people around us so if you stress yourself on some of her habits, you will also stress her, although she might not be able to describe what she really feels.
Sorry if I seem self-important, I really don't mean to be. I just hope my stories might easy the life of some fellow aspies and their relatives.