My son is also allergic to dairy and eggs, so I can totally relate (he had anaphylaxis from a small amount of dairy at 8 months, and is much less sensitive now, as we get his blood tested at Hopkins annually, but still he avoids it totally since he still reacts and we do carry epipens and always will).
Just a little reminder (although I'm sure you always do this) but even ordering pasta plain let them know about the allergy. I'm saying this, as my son now drives me crazy when he fails to tell a server he has allergies (he's 16 which is a hard age, they think they're invincible sometimes at this age) so even if he orders what he feels is safe, they need to know about the allergy. We've (rarely but it happens) been to places where the pasta has some egg in it - but if Disney knows they will ensure your safety! This is one reason we have taken so many trips there - they will change gloves even so there's no cross contamination.
I'm sure you'll do fine it sounds - but sometimes it does get hard when the choices are limited. We've found some counter service places go over the top to make sure he can have something nice, where others are so busy (but we usually by now know where he can get something he likes - BOG is so new that it's hard to find reports of allergic folks and their choices).
I wish you a good safe trip!!