Well, after hours of troubleshooting, changing settings in Windows, on the receiver, etc I think I finally solved it, although it was by accident.
I had everything on and running. Turned off the TV, sound quits out of my Onkyo receiver, as expected.
I RDP into the PC to poke around and play with some more settings and notice that the Sound icon in the task bar has the mute symbol. Of course it never has this when the TV is on, because it's not muted. It's only there with the TV is off and I therefore can't see it. I un-mute it, sound comes back. Disconnect RDP, turn TV on and back off again. After a minor delay sound is now running with TV off.
Still need to reboot to make sure it sticks, but hopefully this helps someone. Will report back if the issue returns.