Not familiar with paper mill operations that much. What I do know, the water used in processing can be very corrosive in some of the processes. That's the reason for using 316 SS. It's either this one or go to a duplex stainless steel. The 400 series is probably out of the question. The PH series may work, be a little bit easier to cut in the 2H1150 condition for 17-4PH. I'm sure the paper mill has gone thru all of the options of materials over the years and settled on 316 ss.
On the wire size to use, you may have to cut a flat on the wire so it will clear the root of the thread. 3/8" drill rod will be too big. Need something in the range of .3125 to .3440". Ken