Any idea when or where he was wounded? THe army was all at Helena about that time and not returned from the battle there so that would not be the place. Wondered if he died of disease or do you have info on any minor skirmish somewhere previously. Grindstead's Regt, the 33rd Ark Inf organized in 1862. The only major battle prior to death was Prairie Grove in Dec 62. See info below from his CSR. THe infantry didn't have too many scrapes with the yankees after Prairie Grove and prior to Helena.

COX, FULKER Pvt - Enl 19 Jun 1862 in Columbia Co, AR. Died 3 Aug 1863 at Little Rock, AR

Most all dead buried in Little Rock wound up in Mt Holly before being moved to either the Confederate Mass mound at the National Cemetery in LR or the mass mound in the adjacent city cemetery (I can't remember the name now but it has a big number of mass burials there.) Unfortunately, there is no listing of names of 99% of those soldiers, so I would say he is either in the National Cemetery or the adjacent city cemetery to the Natl.

Hope this helps some.