Addendum: It gets even easier. The NVidia control panel for the 1660 (and, I assume, other newer cards from NVidia) contains an item "Set up Digital Audio" that allows you to specify which of the (for the 1660, four) outputs for the card will appear under Windows sound settings. So you can run Displayport to your monitor for video and specify that HDMI will appear as a sound source in Windows, running that to your AV receiver. No need to set up a phantom monitor.
Thank you, that was helpful. Looks like I'll be ordering a monitor shortly.
I have the same question. Can I connect my Gigabyte OC Gaming 1660 to a (yet-to-be-purchased) high frame rate gaming monitor (lacking decent sound) with a DP cable and at the same time connect HDMI cable from 1660 to my AV receiver for sound? I don't want to just run the HDMI from graphics card to AV receiver to monitor because the receiver doesn't support high frame rate like the monitor does. (That's how things are currently running, but my monitor is only 60 Hz).