First of all I would recommend tuning the low E string to a D.  There
are three major chords - D, G & Em.  You can play all the D stuff using
the lowest D string.  The G's can be played by strumming only the low
strings pressing the 5th fret on the two lowest strings.  The Em by
pressing the 2nd fret on the two lowest strings.  (Martin seems to
select the strings he strums).
 
Now the end part, starting from the second last "you're such a beautiful
thing" should be G, Em, Cmaj7 (again being selective about the strings
you strum, usually the lowest four, but no drop D in the Cmaj7).  
 
Then it goes into some handpicking.  The first part of the handpicking
still has the C as a bass note and a big stretch to get the melody on
the high strings.  The second chord in the handpicking is an Em7 with an
F# (on the middle D string), then walk down to the F (on the D string),
then walk down to the E (on the D string - a full Em7). Don't play the
drop D with any of these.  
 
The last chord which he uses to climb up and down the frets is done by
strumming the open D on the low string then use a D chord without the
highest D (only two notes) to climb up and down the frets.  The interval
on these two notes doesn't change.  The pointer finger on the G string
would travel the frets as follows:  2, 4, 6, 9, 6, 4, 2 then 2, 4, 6,
11, 6, 4, 2.  That's it, that's all.
 
Simple!?!?!
 
Vicki Charal