I am in agreement with you on the moral factor and other points that you make as to the charactor of the men of the 3rd Arkansas.
Cal Collier made the point that Chickamauga was the nearest that the 3rd Arkansas Boys came to getting back to Arkansas and the only battle that they fought with other troops from their home state. I believe that was some of his assumption to form his explaination to account for these "missing" men.
From reading various accounts of the Battle of Chickamauga it would seem that the battle on September 19th seems to be where most of these missing men disappear.
The position of the 3rd Arkansas on the extreme left flank of the entire Confederate army, on that date in Vinard's Field was extremely exposed to being flanked and faced superior numbers. There are several accounts of charges and counter charges being made across Vinard's field and a promanent feature of that field being a ditch in the middle, in which the wounded of both side sought shelter. That ditch acted as a trench and was evidently the scene of heavy fighting to gain and keep control of Vinard's field.
The 3rd Arkansas and the Texas Brigade abandoned this position after nightfall of the 19th and were repositioned behind the center of the Confederate Line for the next days attack on the 20th. This did not give the 3rd Arkansas time to collect their dead and wounded of that days fight.
We know that the 3rd Ark. did not return to Vinard's field after the battle either because of the federal army's retreat. This would mean that seriously wounded or the dead of the 3rd Arkansas would have been handle by people who would not have known which command those men would have belonged to.
To me that ditch is the "black hole" where those mens were lost.