Could you perhaps disclose the make/model of this USB DAC so we may look at its installation particularities and drivers?
Are you sure the DAC is allowed/supported to work in a virtual environment? (maybe searching the net or emailing the manufacturer could shed some light on that).
If you manage to get the drivers working correctly, I see no particular reason Wasapi wouldn't work - however ASIO is a different beast.
Also, try to use a USB2 port on your host instead of the USB3 I am suspecting you use. I had some instabilities using USB3 ports in my guests, which I have not yet retested under the recent 15.5.5 Workstation release (which includes some USB fixes).
Finally, for the sake of completeness, could you try installing a Windows 7 guest and see whether you have better results there? If the manufacturer does provide Win7 drivers I am predicting success.