Do we agree now?

Yes. You're more or less saying the same things that I wrote here.

But I'm not sure what the difference is between numbered items 1 and 2 on your first list. If the resulting songs all have the same peak volumes in both versions, how are they different?

I understand your point about the difference between analyzing RMS volume versus analyzing peak volume, but if in the end, the files get normalized to the same amount (ie, no peak ever clips and all peaks fall in the same range), then the analysis method doesn't matter. Do you have an example of a piece of software that does #2 without resorting to dynamic compression?