Monty Bates
Mathieson was a tool maker located in Scotland. I have restored a number of plough planes and I can tell you it is a money pit. On some I had to make my own Taps to cut the internal thread and threaded the rods on a lathe. If you are strictly wanting it as a user then converting to metal threaded arms along with Nuts is a possibility. I suppose the simplest way it to just buy another Mathieson Plough plane for parts as they are fairly common. In this technological era I think you would 3D print and arm and hardened it with super glue. All these methods are not cheap, I know I have spent hundreds of dollars restoring a fifty dollar plane