I know that Grant intended the exchange process to cease at some point, but for some reason it continued to some degree. My Great Grandfather, Corporal William M White was, according to his service records, "Transferred from New Orleans, La. and exchanged at Red River Landing, July 22nd, 1864."
As a member of Company E of the 17th Texas Infantry, he and approximately 320 other Confederates had been captured at Fort DeRussy, La., on March 14th, 1864. Along with the artillerist, William's fellow Company E, 17th Texas, a company from the 18th Texas, and a company from a dismounted cavalry unit (I think) were captured when the fort fell.
Thought you might find the exchange that took place in 1864 interesting.