I’d look no further than the oats causing the bloating. We don’t recommend oats, even gluten free ones on the diet because of the starch content. If you were allowed starch, you could eat things like corn, potatoes, and carrots. Oats are also a grain which is to be avoided on the diet as well…this is a grain free diet.
Oat milk is even worse because it concentrates the oat.
Oat bran is allowed on the diet because it feeds the beneficial bacteria in the gut. Oats do not do this nearly as much.
I’ve been on the diet for over a year and still don’t eat oats myself.