Have you tried cotton cord (hat cord about 1/16" or 3/32" diameter. Plain string is too thin)?
The reason most musket barrels don't show a twist pattern is because they weren't made that way, the twist construction being used for sporting guns, but deemed too slow for mass production.
Very early musket barrels were twist construction. But later musket barrels were made by heating a plate of iron, then wrapping it around a mandrel (a bit like placing a hot dog in a roll), welding the seam, then heating and hammering it out to lengthen and shape the tube until it was the right length and taper. Then it was filed or ground smooth and given a preliminary proof; that weeded out a defective barrel before any more work was wasted on it.
Later, as water-powered machinery came into use, the hammering was replaced by rollers. At first the preliminary work was done as before, but using rollers to shape the metal first into a V, then a U and finally an O. At that point, the seam was welded.
Then the barrel went to the barrel rollers. These were large "wheels", several sizes to a shaft. They were paired, with one on top and a matching one on the bottom. Each wheel had its rim shaped in a half circle, so the two rollers combined to form a circular opening. The thick tube, with the mandrel inside, was passed through the series of rollers, being heated again before each pass. When the barrel reached the correct thickness, it could either be tapered with another set of rollers or ground/filed to the final shape. Then it was given a preliminary proof
Still later, when drills had improved but it was still not possible to drill the full length of a barrel, the practice was to begin with a short, thick, round bar, drill a hole in it for the mandrel, then heat and roll it as with the other methods. Since the work began with a bar that had no seams, this was the strongest method yet devised.
But the sporting gun industry was very conservative and so were their customers. They stuck to twist barrels for decades, even after deep hole drills became commonplace and military and "common" rifle barrels were made of fluid steel. The English nobleman who shelled out 80 guineas or more (a guinea was one pound and one shilling - about $220 dollars in today's American money) for a shotgun wanted a sign of careful, custom handwork; a mass produced gun, no matter how safe, was an object of scorn.
Jim