The first verse does not have guitar, it fades in at 0:28 with
    Bb
E|----------------------------|
B|----------3-------3---------|
G|----------------------------|
D|-----3--------3-------------|
A|---1---1----1---1-----------|
E|----------------------------|

Verse:
    F                     G                       A                     Bb
E|---------------------------------------------------------------------------------------------|
B|---------------------------------------------------------------------------------------------|
G|-------------------------------------------------------------------------0-------------------|
D|---------3---------------------3-----------------------3---------------------3---------------|
A|-------3-----3---3-----------3------3---3------------7-----7---7-----------5-----5---5-------|
E|---1-----------1---------3------------3----------5-----------5---------6-----------6---------|

    F                    A                   Bb                  C
E|---------------------------------------------------------------------------------------------------------|
B|---------------------------------------------------------------------------------------------------------|
G|----------------------------------------------0-------------------0-------0--------0--------0------------|
D|---------3--------------------3-------------------3-------------------3-------3--------3--------3--------|
A|-------3-----3---3----------7-----7---7---------5----5---5------3---3-------3--------3--------3----------|
E|---1-----------1--------5-----------5-------6----------6-------------------------------------------------|

    A                   E                     F                   Bb
E|-------------------------------------------------------------------------------------------------|
B|-------------------------------------------------------------------------------------------------|
G|--------------------------------------------------2----------------------------------------------|
D|---------3-------------------5------------------3-----3---3------------3--------3--------3-------|
A|-------5-----5---5---------3------3---3----------------------------5--------5--------5-----------|
E|---5-----------5-------0------------0--------1----------1--------6---6----6---6----6---6---------|

Chorus:
    G                  A                   Bb                  A
E|-----------------------------------------------------------------------------------------|
B|------------------------------------------------3----------------------------------------|
G|---------3------------------5---------------------------------------5--------------------|
D|-----0-------0---0------3-------3---3-------3-------3---3-------3-------3---3------------|
A|----------------------0---0---3---0-------1---1---1---1-------0---0---0---0--------------|
E|---3---3---3---3-------------------------------------------------------------------------|

    G                  A                   Bb                  
E|----------------------------------------------------------------------------------------|
B|------------------------------------------------3-------------------3-------------------|
G|---------3------------------5-----------------------------------------------------------|
D|-----0-------0---0------3-------3---3-------3-------3---3-------3-------3---3-----------|
A|----------------------0---0---0---0-------1---1---1---1-------1---1---1---1-------------|
E|---3---3---3---3------------------------------------------------------------------------|

    G                  A                    C
E|------------------------------------------------------------------------------|
B|-------------------------------------------------5-------5---------5----------|
G|---------3------------------5-------------------------------------------------|
D|-----0-------0---0------3-------3---3--------3-------3---------3--------------|
A|----------------------0---0---0---0--------3---3---3---3-----3---3------------|
E|---3---3---3---3--------------------------------------------------------------|

     D                    C                    Bb
E|------------------------------------------------------------------------------------|
B|-----------6-------------------5----------------------------------------------------|
G|------------------------------------------------------------------------------------|
D|------7--------7---7-------3-------3---3------------3-------3-------3---------------|
A|----5---5----5---5-------3---3---3---3----------5-------5-------5-------5-----------|
E|----------------------------------------------6---6---5---6---6---6---6---6---------|

Bridge:
    A                                       Bb                  A
E|-------------------------------------------------------------------------------------------|
B|-------------------------------------------------------------------------------------------|
G|-------------------------------------------------------------------------------------------|
D|---------3-------------------3-------------------3-------------------3---------------------|
A|-----5-------5---5-------7-------7---7-------5-------5---5-------5-------5---5-------------|
E|---5---5---5---5-------5---5---5---5-------6---6---6---6-------5---5---5---5---------------|

     G                             A
E|-------------------------------------------------------------------|
B|-------------------------------------------------------------------|
G|------------0--------0---------------------------------------------|
D|-------1---------1----------------------3-------3------------------|
A|-------------------------x2---------5-------5--------x2------------|
E|----3----3-----3---3--------------5---5---5---5--------------------|



***Again, these are the BABC  ROOT NOTES I am noting about the lyrics, just as guidance***


(no guitar)
F                 G                    A           Bb
 She wore a black jacket in the winter sun beatdown
  F                  A                       Bb             C
I guess it was early spring and we were in a park in chinatown
A             E           F                  Bb
If I wear the jacket, her chest and limbs all  wrapped around
        A                E              F       Bb
I would soak up all that light into my lining

(guitar enters)
F                G                       A            Bb
  I leaned in to feel the warmth pouring off her skin
     F                   A                   Bb              C
As I tried to breath her essence like it was precious oxygen
    A                E          F                Bb
And she took off her jacket the second we walked in
    A                   E                   F         Bb
And I soaked up all the light from the flourescence


G                   A       Bb       A
What was I supposed to say    to her  
G                A      Bb
  in the grocery aisle, in the air conditioning?
G                   A       C
What was i supposed to say    to her?
      D          C     Bb
I was coming up empty, coming up...


            F                 G       A                          Bb
I was on my phone for half an hour, embleached in the white light  glare
F                  A                 Bb                    C
sitting at the sports bar 'cause the game was playing there
          A                 E                 F                 Bb
and their hometown team was down by ten but I really didn't care
       A                 E                F           Bb
I just soaked up all the light from the flatscreens


F            G             A          Bb
  oh where could my little darling be?
F                  A               Bb                  C
most of the money I've spent, I've spent it in your company
        A                E                     F                   Bb
now I'm looking for some earliesness(?) and my mind won't let me be
       A                E              F         Bb
'til I soak up all that light into my lining


G                   A       Bb       A
What was I supposed to say    to her  
G                A      Bb
  in the grocery aisle, in the air conditioning?
G                   A       C
What was i supposed to say    to her?
      D          C     Bb
I was coming up empty, coming up...


A           A               Bb               A
  all day I did not know if we'd break up or I'd propose
G                            A
we walked out into the april   glowing
A          A          Bb                  A          
come to me now, muse, tell me something I can't confuse
G                                    A
sing me something I'll never lose in   knowing...


G                   A       Bb       A
What was I supposed to say    to her  
G                A      Bb
  in the grocery aisle, in the air conditioning?
G                   A       C
What was i supposed to say    to her?
      D          C     
I was coming up empty

G                   A       Bb       A
What was I supposed to say    to her  
G                A      Bb
  in the grocery aisle, in the air conditioning?
G                   A       C
What was i supposed to say    to her?
      D          C     Bb
I was coming up empty, coming up...


Alternatively, you can tune your G string down to a F and keep the capo.
Your chords will look roughly like this. It's a lot easier to play with minor downsides.
    F    G    A    Bb   C    A    E    F     G   A    Bb   C    D     A    A    Bb   G
E|---------------------------------------------------------------------------------------------|
B|------------------------------------------------1----3----5----6-----------------------------|
G|---0----0----0----0----2----0----2----4-----5---0----0----0----0-----0----0----0----2--------|
D|-------------2----0----3----0---(5)---3-----0------------------------0----2----0----1--------|
A|---3----3----0----1----3----0----3--------------0----1----3----5-----0----0----1-------------|
E|---1----3------------------------0----1-----3---------------------------------------3--------|
  ll   Verse Part 1      ll Verse Part 2  ll        Chorus         ll      Bridge      ll