The Antlers - On The Roof Chords & Tabs

I chose to tab this song in open D because the A notes ring out as if they're being 
played on open strings. Either way, this is as far as I got:

D | ---------------------------------|---------------------------------|
A | ----5----5----4^----0-------0----|----5----5----4^----0-------0----|
F#| -----------------------(0)-------|---------------------------------|
D | ----4----2----2---------4--------|----4---------2--------2/4-------|
A | ----------------------------4----|----------------------------4----|
D | ---------------------------------|---------------------------------|

D | ---------------------------------|---------------------------------|
A | ----5----5----4^----0------------|--4/5----5----4^----0-------0----|
F#| ---------------------------------|---------------------------------|
D | ----4----2----2--------2/4--2/4--|----4----2----2--------2/4-------|
A | ---------------------------------|----------------------------4----|
D | ---------------------------------|---------------------------------|

D | ---------------------------------|---------------------------------|
A | ----5----5----4^------------0----|----5----4----2----2----4--------|
F#| ---------------------------------|---------------------------------|
D | ----4----2----2--------2/4-------|----4----2----2----2----2--------|
A | ----------------------------4----|---------------------------------|
D | ---------------------------------|---------------------------------|
[ Tab from: https://www.guitartabs.cc/tabs/t/the_antlers/on_the_roof_tab.html ]
D | ---------------------------------|---------------------------------|
A | ----5----5----4^----0-------0----|----5----5----4^----0-------0----|
F#| -----------------------(0)-------|---------------------------------|
D | ----4----2----2---------4--------|----4----2----2--------2/4-------|
A | ----------------------------4----|----------------------------4----|
D | ---------------------------------|---------------------------------|

D | ---------------------------------|---------------------------------|
A | ----5----5----4^----0------------|--4/5----5----4^----0-------0----|
F#| ---------------------------------|-----------------------(0)-------|
D | ----4----2----2--------2/4--2/4--|--2/4----2----2---------4--------|
A | ---------------------------------|----------------------------4----|
D | ---------------------------------|---------------------------------|

D | ---------------------------------|---------------------------------|
A | ----5----5----4^------------0----|----5----4----2----2----4--------|
F#| ---------------------------------|---------------------------------|
D | ----4----2----2--------2/4-------|----4----2----2----2----2--------|
A | ----------------------------4----|---------------------------------|
D | ---------------------------------|---------------------------------|

From this point on, Silberman wails on some chords that I can't quite figure out, though 
he occasionally throws in some parts from the intro.


Good luck!