I have more information, but no solution yet, on this issue.
I made the WASAPI output plugin write to disk _exactly_ the same audio data as it delivers to the USB DAC. The audio data being delivered to the device is correct, because with the USB DAC stuttering, the file on disk is still correct.
Secondly, I believe the nature of the problem is out-of-order buffers in the USB DAC driver or WASAPI itself. When the stuttering starts, any change to the playback data (like using the 'Tone' testing tool in Room Correction) is heard as a series of stutters. So while you would expect to hear:
music, music, music, tone, tone, tone, tone, etc.
You instead hear:
music, tone, music, tone, music, tone, tone, etc.
I believe either WASAPI or the USB DAC driver use some sort of circling buffer pool, and they are losing their order.
Like I said, we don't have a solution yet. I'll post here as we learn more.