A Hba1c of 129 is not even on the chart - so any alteration in diet to cut back on the starch and sugar is going to be an improvement. I was told that they were the healthy foods for so long, and yet all the time I felt ill when eating them.
I suggest taking stock of the carbs in your diet and reducing them a little each week - as it would be too much of a shock to just drop them from the menu.
You might find that you are able to eat more carbs with less effect at one end of the day. For me it is the evening, so I have just a few carbs at breakfast and the rest in the evening.
Your meter will be a great help in doing the fine tuning, but at the moment the obvious targets of high sugar foods, including fruit, and the high carb foods such as bread and potatoes, pasta and pizza should get the heave ho in favour of lower carb berries and veges.