Conclusion 2: If you cannot lower the shutter speed then you must raise the ISO to obtain proper ETTR, and in this case a higher ISO is better. But if you can lower the shutter speed and reach a lower ISO, and do the same proper ETTR at that lower ISO, the image will be much better.
This is correct, but I think your understanding of what I was explaining is flawed

When ascertaining the results of shutter/aperture/ISO (exposure triangle), only 1 option can be examined at a time, the other 2 must remain the same.
ETTR works by increasing exposure to the sensor saturation point.
So by saying the lower ISO is better, and showing the results of this with a slower shutter speed also, the result is flawed, as the lower ISO also has the advantage of a longer exposure from a slower shutter speed.
A true test of ISO (in ETTR) is to have a set shutter and aperture that doesn't change.
Below is a quick test showing my dirty table.
All shots were with a shutter of 1/15 and an aperture of f/4.0. Note: A minimum shutter and aperture must be taken into account. In the field, we cannot just set whatever shutter/aperture we want, as we are limited by our DOF requirements and minimum shutter if handheld etc.
note: The post exposure results are direct from ML and performed in post, and the image sizes are the crops.
ISO 100 - post exposure +2.25EV - 211.05KB
ISO 200 - post exposure +1.26EV - 174.39KB
ISO 400 - post exposure +0.22EV - 154.07KB
ISO 800 - post exposure -0.77EV - 146.94KB
ISO 1600 - post exposure -1.79EV - 143.27KB
ISO 3200 - post exposure - -2.79EV - 142.42KB
And some examples from a copped area that was further in the shadows.Exposure results are the same.
ISO 100 - 212.03KB
ISO 200 - 171.75KB
ISO 400 - 148.30KB
ISO 800 - 143.48KB
ISO 1600 - 135.01KB
ISO 3200 - 134.02KB
Some more points to note.
Some ISO's are underexposed in camera and increased in post as I wanted a minimum shutter of 1/15. 1/15 is below the handhold capability of most body/lens/user combos, but felt is was a good speed (with the available light I had for the test) to highlight my point.
Of course a slower shutter would have been better, but it highlights that sometimes you must use a higher ISO for correct exposure, you can't just keep slowing the shutter.
Conclusion.The shadows are where all the action is! The highlights have enough Signal To Noise ratio at almost all ISO's.
It gets hard to see the differences in noise in some of the test results. Hint: Look at the file sizes. They keep reducing the higher the ISO (less noise).
Note, the results below reference a Canon 5D3. The results hold true for all cameras, it's just that other bodies will have different SNR results for different light levels.
The SNR of an ISO bump reduces by 3dB for almost all ISO's. Reference this DXO chart.

In other words, the noise doubles for every doubling of ISO.
Now reference the SNR of all ISO's at all light levels.

Here we can see again, that in the highlights, even ISO 6400 still has a SNR of 30dB, which is greater (by 6dB) then the SNR of ISO 100 @ 1% light level.
And here is where it gets interesting. If we have an exposure @ ISO 100 that results in our shadows being around the 0.1% light level, we can see that we only have 6dB of SNR (ouch).
Now if we take the same scene and increase ISO to 200, we double the exposure, so that 0.1% light level now lies at 0.2% exposure on the Full SNR scale.
ISO 400 0.4%
ISO 800 0.8%
ISO 1600 1.6%
ISO 3200 3.2%
ISO 6400 6.4%
And at 6.4% light level, ISO 6400 has a SNR of around 18dB vs the 6dB of the same shot at ISO 100. Yes, the highlights and midtones will have a higher noise level (lower SNR), but our shadows (where lets face it, all the noise actually is, or more correctly, where the noise is noticeable due to low SNR) OMG. We gained 12dB of SNR just from using a higher ISO. And these results are reflected in the sample images above.
Yes we can lower shutter speed and/or reduce the aperture to achieve the same results, and if the situation allows you to do so, this is the best way to ETTR, but when you can no longer reduce shutter and/or aperture, hopefully I've shown that increasing the ISO can actually be beneficial. It's not simply a case of higher ISO = more noise.
It's better to increase ISO to gain the best exposure, then to increase exposure in post.
And herein lies the advantage of ETTR. Bring those shadows out of the noise (higher SNR) and then as an added benefit, reduce the entire exposure (and the noise

) in post. Win all the way.