Does he like ham or turkey? Have you tried giving him cut up veggies (like carrots/celery/Colored bellpeppers/cauliflower) with Hummus dip? Hummus is tasty and a great source of protein, and kids like to dip things.
Personally I think processed cheese is disgusting, but if you have a picky kid, it's not the hill to die on. Have you tried Cheeze Whiz On celery sticks? Or tried to send him with some kind of processed cheese dip to dip veggies and pretzels in?
Is there a Trader Joe's grocery store near you? they have all kinds of fun pre packaged healthy things. Maybe he might try a california roll?
My kids aren't particularly picky, but my older son has eaten PBJ sandwiches every day of his life (he's in high school now and takes two). He won't tuna or eggs, and I would have been in the same boat as you if Peanut butter wasn't allowed.
ETA: OOOhh I missed cream cheese. Flavored cream cheese on celery sticks, or ham slices rolled up with cream cheese, cream cheese dips -- You can do a TON of stuff with cream cheese!