I've found an interesting relationship between calories, carbs and blood sugar levels that's always held true for me every time I've put it to the test:
If I'm on very low calories, I can eat lots of carbs and get low fasting blood sugars. But if I'm on high calories, enough to cause weight gain, then I get high fasting readings even if on low carbs.
So I'd bet that I could get a great HbA1c by eating a lot of carbs provided the calories were low and I'd been losing weight for three months before the HbA1c test. But I'd almost certainly be damaging myself along the way because each input of food would cause horrible big spikes, because I'm diabetic.
I also read a post somewhere, not on this forum, where someone said they'd greatly improved their average blood sugar by eating nothing but 150 grams of table sugar each day for a week or so. It sounds like a crazy thing to do, but based on my own experience I believe him.
Anyway that's just me and my observations. I don't want it to sound like I'm contradicting you because I quoted you, it was just relevant to what you'd posted. Just goes to show that we all have different metabolisms.