I found a service record for William S. Cochran, Captain, 2nd quarter 1862,Chickasaw Battalion. This is filed with Wm. S. Cochran, Shecoe's Chickasaw Battalion Mtd Vols. Is this your William "L." Cochran?
It appears a number of the men in Shecoe's Battalion were from Grayson County, TX.
In Watie's 1st Cherokee Mtd Vols are:
Name rank age unit enlist where present
George Cochran pvt 2nd Co F 7/12/1862 Ft Davis 6/30/1863
John Cochran sgt 2nd Co F 7/12/1862 Ft Davis 6/30/1863
Lewis Cochran pvt 18 1st Co A; 2nd Co F 7/12/1861 6/30/1863
Samuel Cochran pvt 2nd Co F 7/12/1862 Ft Davis 6/30/1863
William M Cochran pvt 22 1st Co A; 2nd Co F 7/12/1861 12/4/1861 Absent moving families since 6/15/1863
Alexander Cockram pvt 2nd Co D 7/12/1862 Ft Davis 6/30/1863
Charles Cockram pvt 2nd Co D 7/12/1862 Ft Davis 6/30/1863
The first five were apparently Cherokee citizens -- living in the Cherokee Nation when the war began.
On the 1860 Census, R.L. and Samuel show up in the Chickasaw Nation. R.L. is a merchant. Samuel, age 49, is an "overseer" on the same page with several Methodist Ministers and school teachers. One of the ministers is named "John Carr". Where was Camp Carr where members of Shecoe's Battalion enlisted?