Gain-twist barrels...
are certainly nothing new, but they have never demonstrated indisputable superiority over fixed-pitch barrels for any shooting discipline.
Harry Pope made gain-twist barrels for his breech/muzzle loading lead-bullet rifles, but stuck with fixed-pitch for jacketed, high-velocity bullets. I personally believe that the superior performance of Pope's barrels was due more to his painstaking, careful workmanship than the style of rifling he preferred, and that his barrels would have been as good if all of them had been conventionally rifled. Then, too, I cannot agree with his contention that his form of rifling and loading from the muzzle deformed the bullet less: in fact, it forced the bullet from the fastest pitch at the muzzle to the slowest pitch at the breech, and then back, subjecting the engraved surface of the bullet to shearing forces in both directions, as the pitch changed. The plastic nature of the fairly soft alloys he used may have ameliorated the effects to an extent, but even he recognized that this did not apply to jacketed projectiles.
What is not often discussed are several facts about gain-twist barrels and their effects on the bullet itself: the grooves change width as well as pitch. In a cut-rifled barrel, the grooves decrease in width as the pitch increases, because the aspect of the face of the cutter changes as the angle of attack increases: this would seem to be preferable in a mechanical sense because the changes in the engraved and un-engraved surfaces of the bullet (grooves become wider, while the 'lands' on the bullet body increase in width) help to preclude escape of gas past the bullet. In a button-rifled barrel, the grooves must necessarily increase in width as the pitch is increased, because, unlike the single-point rifling cutter, which has an essentially perfectly sharp crest and clearance behind the edge, the button has lands of finite length in order to push-up a standing wave of barrel material, then ride over it and smooth it in passing, and the only way the pitch can be increased is by driving the button at a pitch faster than the basic one engraved in the button's body - the result is that the barrel grooves increase in width and the lands become narrower, which seems less desireable than the case with cut-rifling. Then, too, consideration of the forces on the button in rifling with a fixed-pitch make one wonder how good the results can be from trying to drive the button at an ever-increasing pitch as it is forced through the barrel: button-rifled barrels already suffer from pitch variations due to such factors as varying hardness of the barrel steel and the lubrication of the bore, and attempting to force it to rotate faster than its basic pitch, on the end of a long rod of less-than-bore diameter (which can be deflected measureably with no more force than the hands can apply), is a very uncertain process.
Finally, gain-twist barrels cannot be lapped in the usual way, for reasons already given. A bore-riding lap can polish the surfaces of the lands, and probably remove any burrs left on the edges of them, but there is no practicable process to polish the grooves, which, by increasing pitch and change of width, prevent a standard lap from being pushed and pulled through the bore.
FWIW.
mhb - Mike