Your BG levels are pretty much the same as mine and my last HBA1c was 40, so you are probably doing better than you realise. I rarely see 7's, so if you can keep in the 5's and 6's, you may be where you need to be.
I eat very little carbs, and never pasta, grains, rice, bread or potatoes. I don't measure my intake, but I would guess its 30-40 gm per day and all good carbs from veg, berries, nuts, seeds etc. I do a fair bit of exercise and I would advise you to do what you can. You don't need to go to the gym, just walk several times a day and tone up by lifting a can of baked beans 100 times a day (Don't eat the beans
) Seriously, it's about keeping active. Your muscles burn sugar when they work.