1. Oh Nana!
Go for the karaage and the tempura, both fried in a fully gluten-free kitchen, and add the daily set if it is running. Oh Nana also cooks low-FODMAP friendly, so it is gentle on more than just gluten.
Owner Nana has coeliac disease herself, which is why the entire place is gluten-free and why the fryer is not a landmine. That makes it one of the few spots in Tokyo where fried Japanese food is actually on the table for you. It is a small room in Kanda, so book ahead for lunch or dinner.