I figured it out!
You can't run both cables near each other. They interfere with each other. There is no shielding on these cables. I'm not sure exactly why, but basic principles of electromagnetism could explain why I heard frequency dips. Just basic constructive and deconstruction forces maybe.
I was careful to keep them away from the floor and other cables, especially power cables, but not from themselves. Separating them brought all the sound clarity I was hoping for, and placing near each other again repeated the problem.