The 37th Alabama and other elements of Moore's Brigade assembled in parole camps at Demopolis during late August and early September of 1863. The regiment was hastily rearmed, declared exchanged about Nov. 1, 1863, and sent to Chattanooga:

http://gen.culpepper.com/military/civilwar/AL37/1863Jan-Dec.htm

I cannot locate the article at this moment, but someone did a study of three Civil War era muskets found in a cave on the side of Lookout Mountain. Due to their type and location, these are assumed to have been issued to members of Moore's Brigade from the Selma Arsenal. Two were flintlock conversions, one of these identified as a French import manufactured prior to the Revolutionary War. The others were U.S. manufacture, one dating from 1816, and the other I've forgotten.

I'll try to post this article later.

Enlisted men surrendered at Port Hudson were exchanged, but officers were taken to Johnson's Island where they remained until the end of the war. Confederates captured in the second half of 1863 generally were not exchanged quickly, certainly not those captured at Chattanooga, who were sent to the newly established facility at Rock Island.

Record of the Exchanged Battalion may be of interest. These are filed among papers of Confederate commands, M331, and include members of the 49th Alabama Regiment. Survivors formed Companies “D”, “E” and “F” of the Exchanged Battalion, serving as provost guard at Cahaba, Ala., until May 1864.

A few members of the 54th Alabama can also be found on these rolls. A detachment led by Lt. Joel P. Abney of Company “C” surrendered with the garrison of Vicksburg on July 4, 1863. Abney’s men were not exchanged until the early summer of 1864, severing with the Exchange Battalion in the meantime.

Mr. Simmons can address issues concerning exchange and/or retention of Confederate prisoners at Fort Delaware &c. following the Battle of Gettysburg.