I'll vote for rifling. From the straight grooves down the barrel in order to provide a "space" for fouling, to the idea that, gee, if 30 inch grooves in a thirty inch barrel work to ease the fouling problem, why not make the grooves even longer by twisting them along the length of the barrel?
"Holy cow, it's more accurate!" (Even with round balls.)
From there, it was but a short step to elongated projectiles, which had greater sectional density (so they would carry further), greater accuracy (so fewer projectiles would be needed), and which could carry a greater payload, in the case of artillery shells.
Without that increase in accuracy and without that increase in carrying power, there would have been little impetus to develop anything further in the same time frame.
I think interchageable parts would have been developed anyhow, disunirregardless of their use in assembling firearms, so I don't see that as being all that important in their conceptual development as firearms.
Terry, 230RN