I owe Asus an apology! The coil whine is from the PSU, not the Strix.
I just took out my Corsair HX850i and ran it outside the case. It's pushing out just over 320W, but that's clearly too much for it. The GPU is fluttering a little, but I think it would be masked inside the case. I guess the 1060 that was sitting in that slot just never stressed the PSU enough for me to notice before.
Sorry Asus! And thanks for your time, sages on this thread!
(And Menta38 - I hope you find a solution to your noise as well!).
Any recommendations for a good quiet PSU?