After a year of reading everything I could find, and too many trial-and-error attempts, I may finally have found the answer. The process is extremely convoluted, hidden, and frustrating. Here is the process, commands, results, and solution I have discovered...
1/ Finding HDMI output
$ aplay -l
returns...
card 1: NVidia [HDA NVidia], device 7: HDMI 1 [HDMI 1]
Subdevices: 1/1
Subdevice #0: subdevice #0
2/ Testing for the correct card
$ aplay -D plughw:1,7 /usr/share/sounds/alsa/Noise.wav
... if noise is heard, then card+device is correct
(do not proceed until you have found the correct card+device)
3/ To find the pulseaudio sinks in your computer
$ pactl list sinks
returns...
3 alsa_output.pci-0000_01_00.1.hdmi-stereo-extra1 module-alsa-card.c s16le 2ch 44100Hz
4/ Manually configuring PulseAudio to detect the Nvidia HDMI
sudo gedit /etc/pulse/default.pa
type these lines at the bottom of default.pa ...
"load-module module-alsa-sink device=hw:1,7"
"set-sink-port alsa_output.pci-0000_01_00.1.hdmi-stereo-extra1"
save and close gedit
Restart PulseAudio:
$ pulseaudio --kill
$ pulseaudio --start
open settings, and check the sound settings
is the correct audio device listed?
5/ switch machine power off, then on to restart
open settings, and check the sound settings
is the correct audio device selected as the default?
if yes, done !