I think the lab test results will be reasonably accurate.
You can always use another lab to cross check, for your own peace of mind..
Use
https://www.diabetes.co.uk/hba1c-to-blood-sugar-level-converter.html to work out what your average BG should be to give any HbA1c result.
People have gone into remission without using a CGM, which is relatively recent.
[Although as a T1 that isn't an option.]
If you are struggling, though, a CGM is very useful to work out where you may be having peaks which you miss by finger pricks.
You should only need one to give you a good overview of where your BG is going throughout the day.
It might help if you gave a sample daily meal plan.
Sometimes reducing your carbohydrates by a lot still doesn't take you down to low carbohydrate levels.