Yeah, common problem. Aside from inletting, opening up barrel channels is another challenging workholding task.
I'm drawing up something similar to what Graco uses here (I had called them about this, for installing their cheekrest hardware), if you FF to about 1:30 you can see a relatively simple fixture that can be clamped in the milling vise, instead of a plate affixed to the back of the stock, could just use another clamping arrangement like the forend.