I was told by a chef at Tokyo dining that at least the Sushi rice does contain gluten. I've read great reviews of food allergies at Teppan Edo. It's one of the few non-Disney owned restaurants that people with food allergies do seem to recommend. I'm quite surprised to hear PP's experience witnessing the food being cooked at a different end of the grill as other food. That could be deadly for some people. I've always read that they cook allergy foods in the kitchen in an allergy area. I wouldn't trust food being cooked at the same time on the same table. Imagine how easy it would be for a drop of two of soy sauce to splash over to the other food or how easy it would be to grab the wrong cooking utensil.
I will explain a little more what I saw because it was not at all what you are imagining. There was no chance of contamination at all.
All the food is cooked at the table in front of you on large grill surfaces. We were the first group for the lunch seatings after the restaurant opened for the day, so the cooktop had not been used for the day.
Here is a picture of the tables with the cooktop in the center.
The guest with the shellfish and soy allergy was seated at the short side of the table closest to the front in the picture.
The other person with special needs was a vegetarian, seated on the long side of the table.
Two specific meals were cooked first for those 2 guests. After those 2 meals were cooked, the chef went on the cook the food for the rest of us.
The person with the shellfish and soy allergy ordered chicken, which was cooked at the end of the table closest to where she was seated. The vegetables for both that guest and the vegetarian were cooked at the other end of the cooktop (to keep the vegetables away from the chicken for the vegetarian - who had no allergies).
After the chicken and vegetables were cooked, the chef served the person with allergies first, then added some sauce to the remaining vegetables before serving them to the vegetarian. There was no soy sauce used until after the food had been removed for the person with allergies. So, none of the utensils had been used to cook anything other than chicken, noodles and vegetables until after the person with allergies had been served.
After both of those meals were cooked, the chef went on to cook the food for the rest of us. I had shrimp, which was cooked last. It was cooked on the side of the cooktop farthest away from the person with allergies.
After everyone had been served, the chef went through a sort of ritual cleaning of the cooktop that involved a lot of scraping, scrubbing with wet cloths and what looked like steel wool pads, then more water. The cooktop looked the same after the cleaning as it was when our meal started.
After the cleaning, all the soiled utensils were taken out. I did see clean utensils brought out for the next meal, so there would not be already contaminated utensils being used to cook the meal for the next table of guests.
The staff there seemed very aware of allergies. Before we ordered, the waitress asked each diner whether or not they had any allergies or special diet needs. Before beginning cooking, the chef checked with each diner to make sure that he knew what our order was and asked each of us again whether there were any allergies or special dietary needs. I do not know whether either of the guests with special needs had made any requests ahead of time, but the chef did spend some time talking to both of them (I could not hear what was being said, since we were at opposite sides of the table.
I was able to get in touch w/the Contemporary bakery recently b/c I had their email still on hand, and I will probably email the chef from Japan whose email I still have (lesson learned, save all those addresses!) I think Brenda is gone from special diets, which is too bad b/c she was awesome and so very helpful at connecting you w/other areas. 
