This might not be perfect.

Verse:

[ ]
E|----------------------------------------------|
B|-7---5---3---2---0--0--3--0---0--3--3--2------|
G|-7-----0---0---0----0--2--0---0--2--0--2------|
D|-0---0---4---2------0--0--2---2--0--0--2------|
A|--------------------x--x--2---2--x--x--0------|
E|--------------------3--2--0---0--2--3---------| *

From the * onward, he continues fingerpicking, but fingers the chords the traditional way.
I think it's probably easier to just listen to the recording and hear what he's doing than try to untangle me trying to write it out in a tab.

Alternate Riff:

This is usually played on its own, but once is used to replace the part in []s above. 
at the bottom of the tab.

E|------------------------------------------|
B|-7--5--5h7--------------------------------|
G|-7--0--7----------------------------------|
D|-0--0--0----------------------------------|
A|------------------------------------------|
E|------------------------------------------|

Break:

There are multiple instruments here, but this sounds the
best on one guitar to me.

I'm pretty sure Dave is either doing this, or
just picking the chords while other instruments do the melody. It's hard to tell.

The way I play it, I just simultaneously fingerpick
all the notes together that line up vertically in the tab below.

Your mileage may vary; if you think something
else is going on here, feel free to tab it out.

E|------------------------------------------|
B|-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-----3--2---|
G|-------0-2-------0-2-------0-2-----4--2---|
D|-0-2-4-----0-2-4-----0-2-4---------4--2---|
A|-------------------------------4-2-2--0---|
E|------------------------------------------|

E|------------------------------------------|
B|-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-----3--2---|
G|-------0-2-------0-2-------0-2-----0--2---|
D|-0-2-4-----0-2-4-----0-2-4---------2--2---|
A|-----------------------------------2--0---|
E|-3-3-3-3-3-3-3-3-3-3-3-3-3-3-3-2-0-0------|

The last A in the break goes back to "a comfort to count the battles won".