Std GP butt will handle the forces OK if the grain structure is good and the wood not horribly soft and punky from oil seepage. Keep the draw-bolt tight. Depends what fits you, as to felt recoil, too. Personally I detest mercury or other butt-mounted recoil reducers - unless a counterweight is added in the forend to balance the gun then it'll be extremely butt heavy. Building a gun to the desired correct weight for your intended load, and to the correct balance, is a much better idea than mercury recoil reducers IMO.

I've only got experience of custom profiled barrels on GP's. GP actions are not heavy, so to me personally barrel profile is very important. Not just the weight, but the weight distribution. I prefer a profile with relatively thin muzzles which has a "concave" taper (swamped but not with a bell-ended muzzle) not a straight taper, and a bit more mass around the chamber. That way the weight gets exponentially greater towards the chamber.

Jon Jongmans makes 12G barrels in your state I believe.