I was never able to get approval on weekly coverage. I went through two appeals (including the letter from my GI, as you did) and they wouldn't do it. I have Blue Cross/Blue Shield of OR. I did not take it to legal level. I had done weekly shots for a month and it was an improvement over bi-weekly, but still not remission. Maybe it was too short a time. But without coverage... I never thought to try going through Abbott!
Good luck! If you find a way to get approval, I'd like to know what convinced them!
Also, I wanted to say that there are others on here with coverage for weekly shots. I don't want my post to be depressing! Just commiserating!