I went from 14% to 5.5% in 3 months with low carb (<100g/day in the 2nd & 3rd month), exercise, a teeny amount of insulin for a couple of weeks, and the dreaded eyesight loss for a month or so as it was so quick, so I'm probably a success and a failure and maybe not exactly what you need
But as you are on insulin, then I would hazard a guess that you 'just' need to balance that correctly to your food/carb intake - I am no expert on that, but know its's not so simple! For the logic of averages though, you could swing wildly from high glucose to hypos and still get a good HbA1c, so not sure of the logic for your medical.
Good luck in getting the results you need!