This song’s strange chords become easier to make sense of if you keep in mind a few things:

1. Brian leans hard on inversions to confuse us, and tricks learned from 40s jazz and classical.
2. The key is E major, but the verses begin “in the ii key”.
3. The whole instrumental vocal section is just transposed up to A major.

The intro ends with a taste of the chorus.

IV  I     ii    IV
A   E/G#  F#m7  A/E

Brian then slides this A/E up to D/A, which doesn’t make a whole lot of sense in E major; he’s heading to the ii key (F# minor).

He starts with b6, 2, 1 in F# minor, then he returns to the home key of E major with a more standard jazz ii – V – I, but with more inversions to make unusual bass voice leading:

f#: bVI    ii        i
                  E: ii     V       I
    D/A    G#ø7/B    F#m    B7/A    E/B

Those inversions are key here to keeping up a bit of tension, and he won’t release that tension with a root-position chord until the chorus. Let’s carry on:

I    vii       I    vi
E/B  D#dim7/C  E/B  C#m/A#

Almost everyone calls this second chord “Cdim7” but really this is the leading tone °7 chord of E with notes D# F# A C. Mostly diatonic to E major. Even though the bass rises, the harmony is really dipping down into the vii° and back to the tonic.

(Now consider “Cdim7”. It has the notes C Eb Gb Bbb because it’s the vii of the nasty key Db minor (Db Eb Fb Gb Ab Bbb Cb). All the flats alone should be a clue this doesn’t make sense in a sharps key like E major. I’ve found naming dim7 chords correctly has helped my understanding of them greatly. YMMV.)

That last chord is sometimes written “A#ø7”, but here it’s not really functioning as A# half-diminished, which would move to D#7 – G#m. This is really just a C#m chord with the bass on the 6th to give it extra flavor (hear C#m – A – E vs C#m/A# – A – E). This 6th-in-the-bass is done all the time on minor chords in 1940s standards to add tension that can then be released, just as Brian does when A# falls to A for the chorus.

The verse repeat is followed by a full transposition up a 4th, playing the whole verse and chorus in A:

B: bVI  ii       i                                       
              A: ii  V     I    vii       I    
   G/D  C#ø7/E   Bm  E7/D  A/E  G#dim7/F  A/E 

A: vi      IV  I     ii     IV
                        F#: bVI  ii
   F#m/D#  D   A/C#  Bm7    D/A  G#ø7/B ...

Notice when Brian ends up at D/A, he seizes the opportunity to jump right back into the original F# minor bit of the verse. That’s how he manages to end the song in E major.