A lot less than a new rifle.
Cost would depend on the barrel manufacturer, taper, bore diameter, length, twist, fluting, chamber (Example, your smith may not have a reamer for an edge etc.)
Any way you put it, its less than or very near equal to the price of a new rifle depending on your choices of "upgrades". Plus you have a guaranteed shooter, in your specs, vs a factory rifle with questionable accuracy. You get a good one, or you don't.....
Re piping is THE WAY TO GO!
I'll fling you a P.M.