I did a tandem skydive a few yeas ago.
Initially, I didn't think I needed a doctor's certificate because the company I was jumping with emphasised age (need a certificate if over 40 years of age) but hidden in the darkest depths of their website I found something which also mentioned medical conditions including diabetes.
I expected this to be a formality and dropped the form off with my GP to be told I had to make an appointment.
At the appointment, the GP (who knew nothing about my diabetes control) was more concerned by me having a hypo than looking at anything like HbA1c. At one point, a thought he was not going to give his consent when he said that I was going to have all the fun whilst he took full responsibility. Thankfully, consent was given after his long lecture and I had an amazing day.
I hope you get the chance to job - jumping out of the plane is scary but once you're out it is a wonderful feeling.
Fingers crossed for your latest blood test results. Hopefully, showing your doctor your recent improvements will show him you are motivated to controlling your diabetes.