Oats are high in starch like carrots, corn, rice, potatoes, and other stuff you have on the diet so you shouldn’t have them in large quantities.
If you want oats, I would consider trying out oat bran which is a prebiotic that feeds the beneficial bacteria in the gut.
Brown rice shouldn’t be consumed in large quantites on the diet either until stage 3 when you basically aren’t doing the diet anymore. Brown rice contains sugar, is high in starch, and high in the glycemic index.
I would examine consuming teff which provides protein as well as over a few hundred kinds of bacteria. It also has great weight gain properties. Its a prebiotic that feeds the beneficial bacteria in the gut.