Bob, I thought of another possibility -- many Union soldiers were reinterred after the war, so perhaps that accounts for why there is an interment record at LR National Cemetery, but no presently marked grave....???

According to the muster roll of the 2nd Arkansas Infantry, U.S. Volunteers, for June 30, 1864, Pvt. Asa J. Shrum was reported to have died of disease at Camp Huntsville in Madison County. Assuming that report to be true, it would seem more likely for him to be interred at Fayetteville, rather than Little Rock.