I have it working now. The Realtek audio driver kits are available in two flavors: a "disable" and an "enable" version. Apparently the "enable" version is to be used when the audio DSP is enabled in BIOS. I had used the "disable" version.
After installing the "enable" version, the hardware (plug-and-play) ID of the HDMI audio device magically changed to something in the ven_8086&dev_2809 to 2812 range which is supported by the graphics driver that you linked in your reply. I've never seen anything like this but whatever... It works now.