Thank you for confirming my feeling that the alleged payment date of 19 November 1864 is a transcription error for 19 November 1863.

That being the case, I think the probable sequence of events is as follows:
-- On 13 February 1864, George had just received his pay for the months of November and December 1863.
-- On 20 February 1864, Cheatham's Division left Dalton GA by train on a bit of a wild goose chase to Demopolis AL. With money in his pocket and being so close to home in Ducktown TN, George decided not to board the train and crossed over to the nearby Federal lines.
-- He took the Oath of Allegiance, and was released at Chattanooga TN on 27 February 1864.
-- Unfortunately, it appears as if he failed to make it home.
-- In the meantime, his regiment - the 19th Tennessee Infantry, not knowing that he had deserted - continued to report him absent on a detail (at Divisional HQ) for the muster rolls during the first half of 1864, until the news of his desertion finally reached them and they recorded his status as such in the muster roll for July and August 1864. By that time, unfortunately, poor George may have been long dead.

Every time I read my notes about George, I experience strong resonances from "Cold Mountain".