Gremlin, I sympathize and feel your pain. Short of buying in bulk with the beef (like a quarter cow at a time bulk), and trying to take advantage of either growing your own vegetation or utilizing cheaper local growers through a co-op or CSA and thereby going with more seasonal eating, there's not much more you can do on the food front than that. Unfortunately, this sort of allergy setup is best handled through a more raw and unprocessed diet which in a way means reverting back to a pre-industrial food chain.
That said, first, experiment around with kosher foods... especially on the meat end. Kosher's not just a specific form of humane slaughter, some cases the animal is checked for health issues in the lungs (glatt kosher), it's also drained of blood and lightly salt cured to try and remove any remaining blood from the meat... if you can find it and when done properly, grass raised and finished glatt kosher beef is basically the best you'll get. Personally, I find it tastes better, and there's been studies that indicate that the meat digests better and is healthier with a majority of the blood removed and nearly none of the high-stress hormone cocktail released by the animal before death when done right. You might find your son has an easier time handling this sort of meat, both beef and chicken. A place to start regarding this research would be with Dr. Temple Grandin, Professor of Animal Science at Colorado State University. Her website is here in all its retro 90's glory:
http://www.grandin.com/I know there's a milk allergy there, but frequently dairy allergies in humans are directly related to cow's milk specifically, and not mammalian milk in general. Do you know if goat's milk is safe? If it is, that might potentially open up an entire world of milk and cheeses to the diet if you can start keeping a milk goat around or know someone who does. If it isn't, it might be additional ammunition to my posited hypothesis below. In a similar stripe, what about lamb as a meat as well?
Beyond that, embrace what Mary said. Don't try to find substitutes, embrace what you have to work with. That'll go a way to reducing budgetary costs.
As a final aside, it also looks like the kid has a problem with the nightshade family given the tomato, eggplant, chilli/capsicum, and potato allergies. If you aren't already, it might be best to keep him away from tobacco exposure as well given it's part of the nightshade family. Given the other allergies, I'm also guessing that he has problems with bananas, avocados and sesame seeds as well? I am
not a doctor, but I only intrude and inquire as it appears there seems to be a thread with
some most of the allergies and possible
tyrosine metabolism issues, which if proven to be more than a corollary coincidence here would impact dopamine and other neurotransmitter levels, the ability to better absorb other key amino acids, and impact thyroid function. If you can nail down the possible root cause, it makes it much easier to know what's safe... not that I'd advocate experimenting needlessly if at all, but it might be an idea worth floating with a specialist.