Anthony, I'm not 100 percent certain, but as far as I can tell, the J. J. Taylor who served in the 1st Arkansas Mounted Rifles did not subsequently serve in Co. D, Carroll's 4th (aka 1st) Arkansas Cavalry, so that still leaves John Jackson Taylor on the table, as you suggested. The Texas pension record and memorial inscription would seem to point to him as being in Carroll's regiment. If those other Taylor men who served in the same company could be tied to John Jackson Taylor, that would just about clinch it.