I find it odd that G. R. Tucker did not mention Jackson in his autobiography. He was helping his brother farm near Burlington, later renamed Spanish Fort, and the town council offering him the job of constable of Spanish Fort which he accepted. He was paid $5.00 per day plus expenses being the town was so wild. He did mention many cases of dealing with whiskey runs and outlaws in general but nothing about your Jackson.
I wonder what a Deputy U. S. Marshal was doing at Spanish Fort? They only left Fort Smith with warrants and had no authority in Spanish Fort, only Indian Terroritory. Therefore, you story has some problems. Also, had a deputy shot him, the deputy was automatically arrested and had to be cleared of all shootings in court. I find no Deputy in the archives charged with your Jackson shooting. I do not deny that he may have been shot, and in the back, but I doubt it was by a marshal unless he was in I. T. and part of a gang that a deputy had warrants on.
A Deputy marshal worked for no salary before 1896. He was paid a small fee of about $2.00 to serve warrants and paid milage of .11 cents [from memory] per mile. If he killed someone he had to pay for the burial and was held accountable to the courts to clear himself of murder. Rarely did a deputy return to Fort Smith with a body. Judge Parkers court was divided with five additional locations and Paris, TX Eastern district was establish in 1889 to work Choctaw nation north of the Red. Again, no Marshal would have legally been in Burlington/Spainish Fort in 1879. That is factual.