You mention HbA1c levels. You might find this link from the Home Page of interest
https://www.diabetes.co.uk/what-is-hba1c.html
62 your latest A1c is still in the diabetic range but a lot lower than the 80 you started out with, so yes its a definite improvement and if you keep on doing what you are doing, I would expect your levels will have dropped even further when you are due your next test.
You also mention TG levels, can I assume you are talking about Triglyceride levels indicated from cholesterol results? Usually an A1c will also include a cholesterol test. If it is Trig results from a cholesterol test, then ideally you want to be looking at levels of under 2.3 if non fasting blood was undertaken or under 1.7 if you fasted before the test. The lower they are the better. Higher levels come with increased risk of stroke etc. If your doc is saying your Trig levels are high, its worth finding out what your numbers were at the last test plus what they were at diagnosis, and do a comparison. If your trigs were fine previously, I would be wondering what's changed - cholesterol levels are actually very dynamic. I can change mine in 3 days just by eating lots of calories - not good for my blood sugar levels though.
When you come to take your next test, your doctor will probably want you to fast as a fasting cholesterol test gives a more accurate result I fast for around 12-14 hours before my blood draw; Trig results can be skewed if you haven't fasted. You might find that if your trig levels show high again at the next test, the doc will probably want to prescribe a statin so it might be worthwhile doing a little research on the subject so if the question does arise you will then be in a better position to make an informed choice. Hope all goes well.
I do hope things go well. Happy to respond to a PM if you have any questions, now it's back to FBG levels.