FWIW, I switched from an "audiophile-grade" USB cable to a generic, cheap one. This was at Jason's suggestion. It's been a couple of weeks, and—knock wood—no screeching so far.
I don't believe that the cable is the root cause, since I'd been using it for months with my previous DAC without any issues. It must be in the way the Gungnir interfaces with it. One possibility is mechanical: first cable is much heavier which puts more stress on the input. Don't know. If/when screech re-appears, I'll post.
... following Jason's advice, I switched too from a Wireworld Ultraviolet to an USB cable *with* ferrite filters on both ends
(... but, please, don't tell him it's the Kimber USB. I swear: it's the only *short* cable with ferrites on both ends I could find ;-p )
so far (10 days since)... it still happens but a) less frequently and b) with less instances, when it happens, in the same session/day
but when it happens, each "screeech" seems to lasts longer (30 sec versus 10-15 with the old cable)
Have you advised Jason of your findings with a ferrite choked cable? Recommending a usb cable with ferrite chokes is the standard response from Schiit. Providing them with this info should go towards isolating the issue if they are working on a solution.