Last night I ate at Baatar for the third time and felt no gluten symptoms, so I feel confident in recommending it even though a shared grill is a risky situation. Baatar calls itself a Mongolian BBQ, but it's one of those places where you put whatever you want in a bowl and they stir fry it on a huge griddle for you. I was able to go on their website and figure out which sauces are gluten free.
I've eaten their Sweet and Sour sauce and Peanut Sauce. Whenever I go there, I tell the cook that I have a serious food allergy and that the grill needs to be cleaned before my food gets put on there. For simplicity sake, I tell them my problem is soy sauce.
Then, I watch while they clean it. They are always very nice about it. They also have some vegetarian options, which is nice.
The buffet, which costs about $8 also includes a salad bar, fresh fruit and Blue Bunny ice cream for dessert. On the Blue Bunny website it says all Blue Bunny products are GF unless they contain an obvious wheat-containing ingredient like cookie dough or cookies and cream.