This is a really awfully laid out blank. The other problem with Turkish blanks is that they are either boiled or steamed for 24 hours which drives out all of the natural oils. This allows them to be dry in a couple months, but they will never stabilize. It is a horrible thing to do to wood.

A 5/16" pin is an excellent idea. It have saved the Weatherby designed stock. But use steel, not a wooden dowell. Epoxy it into place. Poor grain flow only has 5% of the full wood strength according to Mark's Mechanical Engineering Handbook. Be careful of the wrist and action area, especially. Weatherby forgot a pin in a 1997 270 W'by and it was horrible grain in the wrist. It broke when fired and did brain damage to the shooter. I was the expert witness in the case. A 416 is a lot more gun than a 270. Those pins are very good ideas.