I worked this out (with help from the previous version and the fantastic tab) by
listening to James Mercer play it acoustically. I'm 100% certain that this is right. The E74
chord is the same as the one he used in Past and Pending, which is how I came across it. 
Listen to the song for the changes in that chord, and I'll tab it for clarity. It sounds
lovely with open chords, with the obvious exception being the F#, which is easiest (and 
sounds best) played at 2nd fret.

E5   02020x

 E5      B5        E5 - E5   A5
"Howdy, lem ," my grandpa    said with his eyes closed
E5          B5                       E5 - E5 A5
wiping the eastbound dust from his sunburned brow
A5
a life before doubt.

Chorus:
G5           A5                  G5                A5
I smell the engine grease and mint the wind is blending
G5         A5               D5          F#5   G5
         D5    A5
under the moan of rotting elm in the silo floor

Verse 2:
E5      B5        E5 - E5   A5
Down a hill of pine tree   quills we made our way
E5      B5                            E5 - E5   A5
to the bottom and the ferns where thick moss   grows
A5
beside a stream.

Chorus:
G5         A5                    G5               A5
Under the rocks are snails and we can fill our pockets
G5               A5              D5        F#5
G5         D5     A5
and let them go one by one all day in a brand new place

Instrumental break x2
E5 B5 E5 - E5 A5
E5 B5 D5 A5

(play this variation on the verse chords twice)

Chorus:
G5            A5        G5            A5
You were no ordinary drain on her defenses
G5               A5        D5        F#5       G5
and she was no ordinary girl Oh, Inverted World
           A5             G5                  A5
if every moment of our lives were cradled softly
                    A5                  D5
in the hands of a strange and gentle child
         F#5      G5
I'd not roll my eyes
E5       G5
so.

E       G Repeat until fade


When James Mercer played this acoustically, he repeated the E and G at the end a few
times then ended with E G A E which sounds really nice. As usual, Mercer does a lot of
Hammer ons and pull offs, which you can add optionally (sounds great on the D chord just 
before the F# and on the A in the chorus)

Furthermore, The E to E74 change is a quick one. The E and B chords are a bar each,
whereas the E and E74 chords last half a bar each. Listen to the song if timing is an issue.

I really hope this helps somebody out there play this fantastic song :D