Looks like diverticulosis does not require any special diet or treatment?
In addition the diverticuli may resolve after a time gluten-free. I had extensive diverticuli throughout my entire large intestine before my celiac diagnosis. GI said he had never seen anything like it. When I had a follow up colonoscopy 5 years after diagnosis they were almost all gone.
Make sure you check those food based supplements as some will be labeled gluten free but contain barley or wheat grass. You don't want those.