How can I reduce my fasting readings

Thank you for raising this question.

Despite low-ish carbing for 6 months, and a HbA1c now down to 5.8, I still have readings of around 6.5 every morning. Never less than 6.2

Morning readings are fiendishly difficult to get down. It seems that it takes a long while with good day readings before the fasting ones respond. Two things helped me:-
1) I eat or drink NOTHING within 2 hours of going to bed, other than water or, at bedtime, a mouthful of lactofree milk (about half the carbs of normal milk) My snacks on nuts etc are always before this cutoff. This gives my BG time to settle before sleeping. I believe that most T2s on diet only/metformin "flat line" during the night, so ignoring DP, what you go to sleep with you wake up with.
2) I exercise about one hour after my evening meal - just teninutes of HARD exercise. I use an exercise machine, but you could equally just run (fast walk?) up and down stairs for ten minutes. Not a big sacrifice of time, and not enough exercise to cause a possible liver dump, but enough to get my post evening meal Bgs down quicker and further.

It did help. I was always in the 6's fasting, sometimes low 7's, but now i'm low 5's.

We are all a tad different though, and even if you DO wake to 6's,you don't know that your BGs haven't been much better in the night, as DP starts before you wake up!