Criterion offers their match grade 'Remage' barrels in the 340. 1/10 twist.

I've been told that the long-action magnum 700, can accommodate the longer Weatherby magnums by removing a spacer in the mag box.

I'm wondering about the mag box and also the follower.

Does anyone have experience with this?

There is no block to remove from a Rem 700 LA mag box, and the follower is the same for a 7mm Rem Mag as it is for the 7mm STW, which by the way, is the same length as the 340 Wby Mag. The magazine lips may need a bit of adjusting and the rails and feed ramp a bit of massaging, but that's all. Not a big fan of the "Remage" barrel nut system, but I guess they work OK.