According to WDWINFO here are the restaurants that serve grilled cheese:
Earl of Sandwich
ESPN Grill
ESPN Zone
Ohana
Pinocchio Village Haus Restaurant
Sassagoula Floatworks and Food Factory
Tony's Town Square Restaurant
And here are the ones that serve pizza:
1900 PArk Fare
ABC Commisiary
Cape May
Bluezoo
Boardwalk Pizza
Catalina Eddies
Chef Mickey's
CRT
Contempo Cafe
Crysatl Pala
Earl of Sandwich
Liberty Tree Tavern
Mara
Old Port Royale
Pinnochios Village House
Pizzafari
PLaet Hollywood
Portobelllo
Akershus
Rose & Crown
Shutters
TRex
Tonys Town Square
Toy Story
Via Napoli
Trails end
Wolfgang Puck express
They have a great feature on this website where you can put in any food & they will tell you where you can get it. I have 3 very picky kids (1 whose issues are so bad he has a feeding tube) so I found this tool very useful in picking where we eat. I have also started to carry around a couple peanut butter sandwiches for my youngest in case there is still nothing he likes. My kids are all picky in different ways & the kids menus are often very limited so its hard to find a place where all 3 find something they like. Sometimes just having a sandwich on hand is easier.
Also, we ate at CP last year & my youngest (the one with the tube) didn't like anything on the buffet. The waitress noticed & had the chef come out. We told him he would eat a hot dog & he had someone go next door to Casey's & got him 2 huge hot dogs & fries. Exceptionally nice! One other thing that may or may not be relevant- my kids only like Kraft mac & cheese, what they serve at the parks is nothing like that. Its very thick & creamy. Also, a lot of the restaurants serve "meaty macaroni" as their pasta. We thought it looked & tasted pretty gross. Good luck in your search!
On our last visit in Sept. the grilled cheeses were no longer on menu at Pin. Village Haus, Tony's and ESPN. Just FYI for next trip, although they may make something for dietary issues they were no longer on menu.