Brent,
You seem to have somehow missed the point of my comment about custom rifles. If the barrels of Pope, Schoyen, et al would have shot better with a barrel profile that was of ANY shape, that's likely what they would have used. For instance, I've never heard of Pope making a 7 sided barrel although he was quite concerned about the INSIDE of the barrel. He sometimes bought pre-drilled barrel stock from the big companies and worked from there...so we see, for instance, octagon Winchester marked barrels also marked "rifled by HM Pope." BTW, one of Pope's own pet rifles had a barrel with an unfinished round contour IIRC, referred to as "dog fight."
What I meant to imply, but maybe should have stated more succinctly, was that the octagon barrels we all seem to love (and yes, several of my favorite rifles wear them!) are really just a styling throwback and have little or no effect on the shootability of the rifle. The additional machining, if done haphazardly, MAY even introduce additional stresses into the barrel's steel, but it PROBABLY has no effect on stiffening or cooling, or whatever...it is pretty much cosmetic nowadays, and if you want to make it look pretty (as I sometimes do) have at it; but don't expect improved performance out of this feature.
On the other hand, if you want cooling with stiffness and other benefits from the exterior of the barrel, the current research suggests spiral or straight fluting, a larger knob left on the muzzle end, or even a reverse taper. Those methods are outside the scope of this question and get their own thread (and hoots from the traditionalists!
)
Green Frog