Well this is a YMMV issue. I have been VERY successful on CALP (which you haven't read)- on it for 18 years and have maintained my weight loss.
I eat very little sugar- but I love that nothing is forbidden- and this plan works for me. As I said, this is an individual/personal choice and we can chose different paths.
Knowing you are very sensitive to sugar as a trigger, and are trying to manage your insulin and diabetes, this may not be the best plan for you.
Best of luck on your chosen plan-
E