Could the stock be putting too much pressure on the barrel?
Well, that was my first thought all along...that's why I wanted to relieve the stock a little, but the folks at Weatherby told me not to.
It could also be your technique. Be sure to use proper breathing, trigger control, sight picture, follow through, and no cant. That is not to let the rifle tilt right or left while shooting it. Also, be sure your platform is as stable as possible and that your neck is not positioned too high or low on the stock.
I'm sure my technique is less than perfect, but...I'm sitting ona very stable bench, using good rests, and one thing I'll say for myself is I don't flinch.
Stock fit is always a problem for me, as I have a long neck, but...I really don't think that's what's going on here.