Thanks for the guidance, everyone! Indeed, it appears to be GPU coil whine.
Capping the framerate via console commands or Project Settings had no effect; apparently the MoviePlayer doesn’t use those values between levels. Out of curiosity, I also tried using GEngine to cap the framerate in C++ before SetupLoadingScreen() gets called, but even that was ignored.
With how barren my scene is at the moment, MSI Afterburner says I’m getting around 200 FPS in-game and well over 2000 during loading screens. Downclocking my GPU eliminated the noise entirely.