Nice job on the .444. Blending of the barrels is great - is the monobloc seam just in front of the rear scope mount? Hard to tell. Great economical cartridge too - fun I bet.
Buckbrush is on the right track, I think. For me, metal work is easier than stocking a gun, so starting with a pistolgrip stock is the right way to go. Now that I have bought some "real" double rifles, I am more interested in building one myself too.
Keep us all posted on your progress.