I haven't tried it, but my daughter follows a similar, but much more restrictive diet for autoimmune illnesses. She is doing great - off all but one medication. I wanted to tell you to go for it!
The more I read, the more I am convinced that our food supply is to blame for a lot of health problems in our country. People are not getting the necessary nutrients for their bodies to work properly. There are antibiotics, arsenic, hormones, red dyes, "natural flavors" and other stuff pumped into meat. Our produce is full of toxic pesticides. Genetically modified foods are taking over and there are lots of questions about whether these are causing illness. Convenience foods are sorely lacking in nutrients and are full of unnecessary junk.
I think it's a great idea to give the diet a try for a bit to see if it helps. It may be a hassle/inconvenience at first, but it gets easier. I had to cook/puree all my daughter's food the first several months. Now she can eat more variety, but I still have to plan ahead and have food on hand since we can't eat most packaged foods. I work full-time so it was a struggle at first to adjust, but I have kept at it for two years. I don't think you have to go to such extremes on Feingold, but you will find strategies that work for you and your daughter as you get started. If you see results, you will feel so empowered to continue.
Good luck!