A low carb diet is very effective in normalizing type two for me - your long established need for injecting insulin might now be reducing to some extent as the speed at which your BG reduces might be the problem, rather than the actual number. With the lower carbs you just don't need the same amount of insulin, and it is acting like an overcorrection.
I don't need insulin so can't advise from experience, but I have read of a fair few people who have found the same sort of thing happening and have made their own adjustments according to altered needs.