Personally, I doubt it has anything to do with the winding. Let me explain.
I used to spin, both with a wheel and with a drop-spindle. When one is spinning, the rotations cluster in the thinnest sections of yarn, so if the yarn one is spinning alternates from chunky to skinny then the chunky sections are barely spun and the skinny sections end up over-twisted (one reason why people put a lot of effort into learning to spin a fairly constant width of yarn). When plying (that means combining 2 or more strands of spun yarn) the same thing happens, so skinny sections end up more twisted.
Your yarn is plied (you can tell by the two separate and distinctly coloured strands) and it looks exactly the way I would expect it to look if I had handspun the white yarn to alternate skinny-chunky and then plied it with the darker yarn. If you don't like the extra-twisted sections then the solution is not to buy (or spin) yarn that alternates from chunky to skinny, and if you don't like the plied extra-twisted sections then the solution is not to buy plied yarn that alternates from chunky to skinny.
I'm not an expert spinner and a more experienced spinner might disagree, but my assessment is that the phenomena you describe is a natural consequence of the variations in width of the white yarn.
Re. the yarn quantity & scarf length, another alternative is to make it half the width, which will give you twice as much length. I find that very wide chunky scarves are so heavy that I never wear them, so I knit them 5-6 inches wide. So one option - and I don't know how traumatic you would find this - is to rip out the entire scarf and reknit it with 1/2 to 2/3 as many stitches in your cast-on.
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I used to spin, both with a wheel and with a drop-spindle. When one is spinning, the rotations cluster in the thinnest sections of yarn, so if the yarn one is spinning alternates from chunky to skinny then the chunky sections are barely spun and the skinny sections end up over-twisted (one reason why people put a lot of effort into learning to spin a fairly constant width of yarn). When plying (that means combining 2 or more strands of spun yarn) the same thing happens, so skinny sections end up more twisted.
Your yarn is plied (you can tell by the two separate and distinctly coloured strands) and it looks exactly the way I would expect it to look if I had handspun the white yarn to alternate skinny-chunky and then plied it with the darker yarn. If you don't like the extra-twisted sections then the solution is not to buy (or spin) yarn that alternates from chunky to skinny, and if you don't like the plied extra-twisted sections then the solution is not to buy plied yarn that alternates from chunky to skinny.
I'm not an expert spinner and a more experienced spinner might disagree, but my assessment is that the phenomena you describe is a natural consequence of the variations in width of the white yarn.
Re. the yarn quantity & scarf length, another alternative is to make it half the width, which will give you twice as much length. I find that very wide chunky scarves are so heavy that I never wear them, so I knit them 5-6 inches wide. So one option - and I don't know how traumatic you would find this - is to rip out the entire scarf and reknit it with 1/2 to 2/3 as many stitches in your cast-on.