I would guess you could find a Marshall Richards shaving block and then use shaving dies for the size that you desire. Is your rod being cast or rolled to 8.3 mm?
Your rod is about 5/16 inch in diameter. The only rod we used to see that was that size was called ox-off and we drew it without shaving it. The ETP came in 7/16, 5/8, and 3/4. This was before continuous cast so we also had a weld about every 250-300 pounds.
Have you made any rod mounts to see if you have rolled in surface imperfections that warrant shaving? Unless you have evidence of imperfections, I am not sure the cost of shaving to save dies is economically sound. right off the top you are going to have between 6 and 12% scrap. With the current cost of copper that means for every 10 pounds of rod you shave you are going to have about 1 pound of scrap. Plus you will have the added processing cost, the cost of shaving dies, the shaving head, and the electricity to run it.
At this size you are probably using carbide type dies. If you want to improve die life, work with your lubricants. perhaps a good product in the die box that is generally outside of the drawing machine. Sometimes you can just use concentrated lubricant same as what makes up your solution.
A question worth asking is what is your die life? How many dies are in your machine and what is the finish size that you are concerned about.