I've been researching this line...and found several accounts of the deaths of Samuel Trolling & James Barton.
1. killed during the Civil War on the Shy farm encountered by the Adams "gang" while drinking from a spring farm -- A History Of Early Reynolds County, Missouri by James Bell 1986 Turner Publishing
2. It was while they were returning from a Scouting assignment during the Civil War in 1865. After stopping to get a drink of water from the George Stricklin Spring on Neals Creek, that the “Adams Gang” killed Samuel Trollinger and James E. Barton.”
Ozark Heritage Dent County, Salem, Missouri 1851-1978 -- Dave Turner (editor) - Dent County Historical Society 1978
But the most extensive account is given in the autobiography of
Elihu H Shepard - written 1866 & published 1869 by G Knapp & Company, St Louis MO
p.205-210 - CHAPTER XXVIII.LAST DAYS OF THE GREAT REBELLION AND DEATH OF TWO DANGEROUS ENEMIES, AND THEIR BURIAL NEAR KAOLIN.
In February, while this state of affairs continued, two notoriously bad men, Samuel Trollinger and James Barton of whom I had reported to the provost marshal, as mentioned in the last chapter, rode about the country, guiding parties to steal, rob and murder with impunity, until they were both checked in the following manner:
....which states that they were on their way to kill a man named Strickland...Strickland had a party of 4 soldiers ready and they separated when they saw the approach of Trollinger & Barton...Strickland had but one of his men in sight with him, the other four being a little behind, when Trollinger espied them approaching, and, instantly dismounting, both parties posted themselves behind trees and opened fire on each other. The four soldiers, on hearing the firing on their friends in front, separated and ran far round, two on each flank, to prevent a retreat, and, commencing firing, killed Trollinger at the first shot. Barton, seeing him fall, and the present inequality of the combat, attempted flight, but soon fell in between the two soldiers posted on the line of his retreat, and was likewise instantly killed. ...
With the military 8 January 1865 report of their deaths in combination wit these accounts, it would suggest that the fruit jar paper of 1864 is correct.
Now sure how "jayhawks" would have come to the gravestone, as jawhawks was a term used along the Kansas-Missouri border.