I thought the answer would be found in
Confederate Military History. The volume on Alabama is arranged differently than most of the volumes. It has a chapter on War of 1812, one on the political steps to secession, organizing the military and then a short chapter on the entire war. It then has a brief history of every regiment followed by a time-line of every battle, large and small, where Alabama troops fought in. Biographies of generals are at the end.
This is the only thing I could find that mentioned general of the state militia.
Brig-General
Michael J. Bulger moved to Montgomery in 1823. He was elected Major of the Alabama militia in the 1830's. In 1838, he moved to Tallapoosa county.
Soon afterwards he was elected brigadier-general, and held that position until
1861.
Michael J. Bulger
It is odd that there is no mention of an Adjutant General of Alabama or any state militia. I will flip through the unit histories to see if there is anything there.