Bryan,
The Supplement to the Official Records offers scant information regarding the 12th Arkansas.
Remarks that the regiment was captured at Island #10, and that some escapees served in company's D & F of the 6th Arkansas, while other individuals re-enlisted in the 33rd Arkansas.
Nothing at all about yet a third mysterious group of escapees involved as a regiment in that consolidation [12th/14th/23rd Arkansas] of Sept 10th, that you mentioned.
Nobody said it would be easy.