Hi - I used the free Libre trial available from Abbot. It was informative and I'm glad I did it. It's a few years ago now so I'm thinking of buying a few weeks of Libre use, just to see what's happening.
I don't know of anywhere in the NHS that routinely funds CGMs for T2s. It's possible you could get your local NHS to pay for it, but you'd have to make an application and persuade them to treat you as a special case. I don't see anything in what you've said that would make me optimistic about your chances of success.
I think you've had misleading advice on the HbA1c. It isn't an average. It counts the number of glycated red blood cells at the point of test, and that enables a calculation that shows how your blood glucose levels are, based on information from the last three months or so (because that's how long rbcs generally live), which is heavily skewed towards the last month. It's generally accepted to be a better measure than one-off glucose testing, because it smooths out the short-term rises and falls in blood glucose that are normal for everyone.
You should have a look at some CGM graphs from non-diabetic people, because you'll see marked rises and falls in their blood glucose levels in response to food and various other things.