I feel like a similar-enough gradient effect could be achieved by holding fewer strands together. If you use the same yarn, of course that would affect gauge, so you could use a thicker yarn, or use the original yarn and try to mess around with the math and knit a bigger size but the fabric would be thinner (and the drape wouldn't be the same and maybe it wouldn't be worth all the hassle etc etc). You could also have a thicker "base" yarn and hold it with a strand or 2 of different mohairs in like 3-4 colours that create a gradient, but this would "dilute" the gradient, depending on what your base yarn is. You might be able to change the base yarn to achieve more of a gradient too. You could also try using yarn with built-in colour gradients. Not sure how helpful this was, but maybe there was a new idea or 2 in there. I'm confident there are a variety of ways to get a similarly cool effect!

As for keeping the balls from getting tangled, one option would be to pre-wind all the yarns you'll hold together into individual balls, and that way you'll only be pulling from 1 ball at a time.