After posting yesterday, I tried changing audio drivers. I have an RME Fireface 800, which is as rock-solid as they get, but when I switched from the native Fireface ASIO driver to the ASIO DirectX driver, the problems went away. Of course the latency was completely unusable with that driver, but it did playback without problems. Not sure what that means, but there does seem to be some type of driver issue.