Garden Grill is pretty plain to start with, though trying to get something special might be more troublesome or time-consuming there, since it isn't a regular "order-off-the-menu" place, and so its kitchen is structured more like a banquet hall than a restaurant. Biergarten is actually a banquet hall, so again getting something special is a little troublesome. At Teppenyaki, you can talk directly to the person creating your food, while he's (I've never seen any women) doing it, so that's where you'll have the most direct control. Spoodles is always very accommodating, of any dietary requests we've had (and we've had a whole bunch of different ones over the years), but the essential nature of that cuisine is that it is special because of the sauces, so why go there if you're not going to enjoy that? Alfredo's has received such consistently poor reviews over the years that it remains the only Epcot restaurant we've never been to. Beaches and Cream is an ice cream shop that serves burgers, and it never impressed me.
So my suggestion wouldn't be any of those, but rather Rose and Crown, Chefs de France and Coral Reef. Rose and Crown is remarkably good, very accommodating, and features a cuisine that still works well, sauce-free. Chefs de France and Coral Reef are also great choices: Although both rely heavily on sauces, at both restaurants I'd trust that a sauce-free dish can be made well-enough to be worth the trip.
