According to the late Edward G. Gerdes' research:
16h Ark., Co D: McGEE, E.C. - Enl 17 Oct 1861 at Carrollton, AR. Detailed to wait on Cpt Mitchell while he is sick Jun 1862. Captured at Corinth, MS 5 Oct 1862. Died at Iuka, MS of G.S.W. to arm 11 Nov 1862.
16th Ark., Co D: RUSH, WILLIAM W. 2Lt - Enl 17 Oct 1861 at Carrollton, AR. Age 22, born in AR. Wounded and captured 5 Oct 1862 at Corinth, MS. Died of G.S.W. to face at Iuka, MS 23 Oct 1862.
16th Ark., Co G: TAYLOR, M.D. Pvt - Captured at Corinth, MS. Died at Iuka, MS (Oct 1862).
Like you, it is my presumption that those 263 souls buried in the trench at Shady Grove Cemetery are the outright casualties of the Battle of Iuka (Sept 18-19, 1862). The marker for these unknown soldiers reads: "... Here lie 263 of Sterling Price’s command who fell in the Battle of Iuka, 1862. ..."
Although the dates of death for these three men all fall well after the battle, they're the only three so far out of the 16th Ark, that research has identified in association with the Iuka action.
Keep up the good work! Your effort has been netting some amazing results.