^And of course there's the iconic Stairway to Heaven....
I'll just make some comments on a couple of other things you wrote earlier:
"To the best of my knowledge, an E aug (E-G#-C) has the same notes as a C aug (C-E-G#), has the same notes as a G# aug (G#-C-E), they are just different inversions of each other. I think there may only be 4 truly different augmented chords:"
Right, if you move the shape up the frets, you get an inversion of the original at every fourth step.
And diminished sevenths repeat every third step, so there's only three of those. The three that Nelson played in his "Michelle" tutorial, in the instrumental outro, are all inversions of each other!
"I've usually seen it used as a 5th chord on the way back to the root chord - like the first chord in "Oh, Darling"."
I was playing one of their early songs on my guitar a few weeks back where there was an augmented chord like that one, played instead of the dominant fifth. But I can't remember which song. Which was it? It's annoying me that I can't pin it down.