You may want to try GF but with using less corn. Rice has proven to be one of the most easily digested grains, but corn is probably not. Quinoa and amaranth have become staples in my diet. Before I went GF I still had days when my stomach wasn't stable at all, quinoa and amaranth didn't seem hard to digest at all.
The teriyaki sauce I make from scratch. I use Tamari sauce (soy sauce without any wheat), vinegar, honey, garlic, and ginger. So there isn't any wheat in it. I don't follow a low fructose diet (I eat applesauce almost daily).