Again have him look at the menus! Based off your comments I'd have double check Teppan Edo (stirfry typically has mushrooms in it, is he okay with eating around them if they don't leave it out), Sanaa (is he okay with Indian type food, you said he was picky), Le Cellier (every vegetarian dish I've had there has mushrooms), and BoG (again not sure how he'd be with Rataouille since that contains both eggplants and mushrooms and seem exceptionally reluctant to go off menu).
Chefs has an amazing Macaroni and Cheese type entree that should work for him and a veggie lasagna (but I'm pretty sure that contains both mushrooms and eggplant). At Kona, they will sub fruit for the bacon with pancakes or waffles. SciFi has a veggie burger. Jiko has a separate vegan menu that you can look at.
V & A will definitely customize based on preference and should call you before hand to find out that stuff. Cali Grill may do vegetarian unplugged but if they're busy you either need to really emphasize you're willing to wait or be prepared to hear no. (This happened to me at fireworks time because the chefs were all swamped with orders and it takes a while especially when you're adding more restrictions)
FWIW, I am not much of a mushroom person, but I will order something with mushrooms in it, because I'm willing to try them, or just eat around them if need be. It's not the flavor I don't like, so much as the texture. I have eaten twice at Teppan Edo and gone away stuffed. Again, I don't have a problem with other veg being cooked with mushrooms, but if memory serves, each vegetable is cooked separately, but on the same griddle (which I'm sure is an insulting word for that majestic food surface they cook on
).
With regard to "picky", we don't really know what OP means, except in regard to eggs, eggplant, mushrooms and tofu. I grew up with a dad and brother who were "picky". They ate all kinds of meat, but wouldn't touch a sauce or vegetable to save their lives. Fast forward to my daughter who is "picky", which means that she'll eat many meats, and sauces of every kind, but won't touch a vegetable or fruit. She ADORED Sanaa, and I'm pretty sure my dad would have hated it. FWIW, I am not particularly fond of mushrooms or tofu (it would be ok with me if they didn't exist
), and I love eating at Disney World. I am MANIACAL about checking the menus though.
At Le Cellier, I had a good pumpkin or squash ravioli there once. Again, their vegetarian entrees are seasonal, so it's worth checking ahead ... and often. This last time, I had the poutine (shared) and a salad. That plus the bread was enough for me. It's not health food, but it was good.
I cannot help with BOG except to say I ate there at lunch and hated it. BAD french onion soup and a BAD dry flavorless quiche. Not going back there. It's the exception, though, not the rule. I also didn't really like Kona for breakfast, but I'm in the minority. I would think a buffet might be better?