You may wish to correct the information posted for the 1860 census. Jefferson Davis County was created on May 9, 1906, so your ancestor could not have lived there in 1860. He does appear on the 1860 census for Williamsburg, Covington County MS, not Hurricane Creek.

The reference to J. McNeese in the 1st Mississippi Regiment is for James McNease, so that's not the right man.

The reference to the man in the 28th Mississippi Regiment actually points to the same name in the 38th Mississippi Regiment. You may have already noticed the similarities. J. R. McNeese has a service file in Co. "E', 38th Mississippi Regiment. Officers and men were surrendered at Vicksburg MS, July 4, 1863, and paroled a few days later.