Just a semi-educated guess, but when Van Dorn abandoned Arkansas in April 1862, to head to Shiloh so the stories go, he stripped the state of everything he could take. Naturally machinery would have been shipped by boat from Little Rock to Napolean, then to Vicksburg, and then by rail to Jackson. by July 1863 the Battle of Raymond (May 12, 1863) and Jackson (May 14, 1863) would have already occurred. If the machinery was still in Jackson at that time it was probably destroyed by the Union Army when they occupied Jackson. I doubt that the machinery was moved since Grant's move against Raymond and Jackson was mostly unexpected since everything the Confederates had were expecting Grant to attack Vicksburg. If the machinery was moved from Jackson before being destroyed it most likely was moved to the Arsenal at Meridian, MS.

Another question is why did Van Dorn leave behind the machines to make the Arkadelphia and Tyler rifles? Was the shipment of these machines stopped by Roane and Hindman before they were taken out of state?