Thread: Bent timber stock.

Never tried anything this complex but if you heated the whole stock in a bath/steamer I'd expect it to warp/twist randomly. You could try to avoid that by securely clamping all around the butt and the fore-end separately then apply tension in the required direction and use focused steam in the area you want to flex.
Steam may work better if there's no coating on the wood.
Whatever way you decide to do it you may be able to open up the stock and re-bed the action to counter any movement.