If you are under a doctors supervision I am forbidden to give you any advice that may alter a doctors advice. They have little to no nutritional training but their word trumps everyone.  What I can do is point you in the direction of programs getting the results you desire. Those three are Dr. Neil M. Barnards "program for preventing and reversing diabetes" (DVD,book), Dr. Gabriel Cousins "Raw in 30" program (DVD) and "There is a cure for diabetes" (book), and recently The Gerson Therapy has released a program for diabetes (book).  The common denominator in all three programs is a low fat vegan diet. The differences are that Barnard's program is a cooked vegan diet while Cousins' and Gerson's program are raw. All get results but the raw programs have a 75 percent success rate in 1 month where as the cooked version of Barnards get results in 6 months. Big difference. I have gotten people off of insulin in around 2 months using a high raw and low fat vegan diet. I use no oils and nuts. I do encourage avocados and seeds for fats. However, with diverticulitis you must avoid seeds until your body repairs itself through a high alkaline diet. I suggest getting a bulk of your fats from avocados and coconut. I usually limit myself to a half an avocados worth of fat a day.  I would look into those books first and if you are under a doctors supervision bring those materials to him/her and see what they say. I hope this helps!