Mac OS X Dolby Digital 5.1 with Mac Mini [solved]

This is my 2nd attempt of trying to clarify how to get Dolby Digital 5.1 output via HDMI. The previous attempt can be found here. All the information I can find on this subject shows that for some people multi-channel audio works fine, nothing special is required, but then again for some of us this is a pain and its almost impossible to get this working.

Here is my setup:

The problem, like presented earlier is depicted here:

The Audio MIDI setup clearly displays as Sony TV being the HDMI output device. The problem is, that it actually isn't. Here is another screen capture of Audio MIDI setup from my brother's computer:

Whoa! His Mac Mini displays his A/V amp as the HDMI destination. Totally different from what my Mac displays. The only explanation for this is, that my Yamaha takes the TV's spec from the HDMI and proxies it to the Mac and his Onkyo doesn't take anything, it simply presents itself as the destination. If you'd ask me, Onkyo's solution is much better than Yamaha's. Anyway, the amp has to pick up the audio signal to be sent to loudspeakers and do a stereo mixdown of a multi-channel signal to be sent for the TV. So there will be a lot of processing at the amp, why not declare itself as the destination for the Mac. It seems to be confusing.

The Solution

Here is what I did to get proper 5.1 channel sound working from my Mac Mini. The problem is, that I cannot get it back to the broken mode again, it simply stays fully functional no matter what I do. There must be something going on at the amp end and something else going on at the Mac end. For some reason they don't match or they do match and there is very little I can do to control it. But anyway, here are my steps with Audio MIDI Setup utility:

1. In the Mac, set HDMI to Use this device for sound output and Play alerts and sound effects trough this device
2. Confirm that the speaker setup is correct and click the speakers to confirm that test tone does not output as expected
3. In the amp, make sure that the input HDMI is decoding multi-channel audio as expected
• Auto-detect or stereo won't work
• Previously my instructions stopped here
4. In the Mac, at the HDMI, in Format set it as Encoded Digital Audio, the Hz setting is irrelevant
   
5. This will effectively unset HDMI as output device and set Built-in Output as the output device. It also pretty much makes all sounds in the system non-functional.
6. Again at the HDMI, in Format select 8ch-24bit Integer, it will reset the HDMI to Use this device for sound output and Play alerts and sound effects trough this device
7. Re-confirm that speaker setup is correct. At this point the test tone should work from the speaker correctly.
8. You're done!

This fix and pretty much everything about Mac Mini's HDMI audio output is bit fuzzy. Any real solution should be reproducible somehow. This isn't. But I can assure you, that now my multi-channel audio really works as expected.

Any feedback about this solution is welcome!

Update 1st Jan 2014:
The number of channels configured into Audio Setup does not reflect the actual number of speakers you have. That is done in Configure Speakers. I have 8ch (or 8 speakers) configured in the Audio Setup, but this is a screenshot of my speaker setup:

They have different number of speakers! It still works. That's how it is supposed to be.