Why do you have to go low carb? Have you looked into low fat vegan diet? I mentioned in another thread about Dr. Neal Bernard's diet for Reversing Diabetes. I've read the book and it is good and the study showed that most type 2 diabetics got to a point where they no longer showed signs of diabetes. If you want to low carb, I'd say go for it but you might want to also consider the alternatives.
You can't out-exercise poor eating habits.