Try setting the screensaver to black screen and disable the screen sleep in Windows. It's not ideal as the screen stays powered on, but it works. On my LG TV I can turn the image off while keeping the sound, so I sometimes do that.
Adding a PCIe/USB sound card should also work, as you mention.
That's an excellent example of lateral thinking. A blank screensaver does the job very well
An HDMI dongle doesn't help because the audio is still going via the other HDMI output, which still gets put to sleep.
What other HDMI output do you mean? I only have the one on my GPU card.