Unfortunately the GP can only reply with what they know/what they think they know. The letter lists the facts as they see it, which I don't think will help your cause.
GP's are often reluctant to go out on a limb. If they say that in their opinion you are not addicted to alcohol and then you get your licence back and go on to injure somebody whilst over the limit, the GP could be under scrutiny. They will generally therefore only list the facts which, as in your case, are often very woolly.
In my case, the GP questionnaire was filled out by a random GP at my surgery, they only half read the notes and concluded I was dependent. I spoke to my GP who was fully aware of my total situation as I had seen her regularly. She wrote to DVLA saying that I was not, and never had been dependent - however I had previously misused alcohol. DVLA then overruled their decision and reissued my licence. Keeping in touch with the GP is crucial in these situations, generally having regular appointments and LFT's carried out help the cause.
Not what you want to hear, but I unfortunately think that DVLA will not reverse their decision, and they will more than likely demand that you stay abstinent until at least June 2022. I'd start getting the LFT's in from now to help with your journey next year as your GP obviously isn't going to give you the benefit of the doubt...