I agree with contacting Special Diets. I disagree that the lists will be useless. While yes, they don't completely overlap, there are many things that are free of numerous allergens. Once you have a list of the ones that are free of everything besides the preservatives, you'll at least have a list of the brands so that you can contact the companies to find out which preservatives (if any) they use so you'll know ahead of time which products are safe.
You're going to need to get some direct answers from Special Diets to find out about things like rotisserie chicken and other fresh made foods that are not specifically for allergies since those aren't included in the allergy lists they send. It'll likely take repeated emails to get them to recognize that you're actually asking specific questions. Don't give up. Keep replying with your specific questions.
As somebody who deals with laundry lists of allergies, we typically try to do TS in the parks and then CS at our resort. At the resorts, they have a lot more ingredients to work with to be able to prepare something safe so we have a heck of a lot more CS options that way. One exception is Sunshine Seasons in Epcot where they have chefs working there preparing all sorts of wonderful fresh foods. There are some others which probably have one or two items your friend can eat as well but it'll take some research to find out which. I would recommend going over the menus to find out which places have some plain looking fresh proteins (like rotisserie chicken, salmon, ribs) and ask Special Diets about those specific items. Again, you'll have to ask multiple times before you get any kind of answer but you should be able to eventually get an answer.