Barrels are a real specialty to manufacture. Gundrilling rigs are dedicated machines with pressure fed cutting oil running thru the gundrill to the tip. Honing machines for the bores are expensive dedicated machines. Turning the o.d. is fairly straight forward since the traditional barrel contour is a couple straight tapers from the breach end then going into a constant o.d., then blended by hand generally. This is the traditional profile from vintage guns. Theoretically, a modern gun could have any profile that is pleasing and functional, given the advent of tracer lathes and NC lathes.
The project sounds like fun...and lots of work. I hope you've come up with some things that make your design unique and worth the work. Blending of modern tech with traditional concepts is fun.
