That is great work. There is really compelling evidence that lowering your blood sugar (and your A1c) reduces the chance of heart disease. The DCCT study in the 1990s should have put all these questions to rest, but there are still deniers. The latest is the ACCORD study which found increased mortality in their intensive treatment arm. There was an immediate interpretation that it was low A1c that was the problem, but every examination of the study has refuted that claim. Despite that, we still hear about doctors that just don't understand. You may have run into one.
ps. If you have an A1c of 4.5%, then your doctor is actually right, your are running too low.