This arrangement has been "stage tested." Unlike the original recording - there are no pedal tones! The bass progression and chord inversions are the result of careful consideration. A little rehearsal and the intention of the arrangement will become clear. Discussion is in the key of Ab. Block chart references Roman numerals - note there many chords on the flat scale degrees, i.e. bIII, bII, bVII, bVI. Whether they are dominant chords or major, their accompanying scales will have #4 - with the exception of the bIIIs in the bridge - Ionian with 4 as an "avoid note." The bridge could be thought of as a temporary modulation to bIII.
The last 4 bars of the A section ("cadence") are used as an intro and as a tag at the end. The first two chords are basically dominant 7b5 (7+11) chords, the melody is on the 13th. They could be voiced as "slash" chords: AMaj7+4/B and GMaj7+4/A.
The bridge merits some discussion. First, the harmonic rhythm is sped up. The first 6 bars took 12 measures to realize in the ballad version. BMaj7 can be voiced as Ebm7/B, the Bb7 might be realized as a Bb13 (AbMaj7b5/Bb) - whatever "lays" best on your instrument. Measure 5 of the bridge, E7b5 (Lydian dominant) supports a high C# (13th of an E7), a DMaj7b5/E would work. The E7b5 is an accent chord, foreign to the progression, it doesn't, lead to another chord, so the goal is to "relax" back to the BMaj7 in bar 6.
Measures 7-10 of the bridge are back to the original harmonic rhythm (borrowed from the ballad version). The Fm7 (melody is on the 9th) inversion is maintained for two measures while the bass walks up to Bb. Drums (and other percussion) buoy things up with accents under the Bbsus, two eighth note pick-ups and long sustain on the Gb13 "surprise" chord. (EMaj7b5/Gb? Press roll bar 9?) Backing up for a moment: the bass anticipates the Bb ("an" beat of 4 in meas. 7) and remains on tempo in bar 8. Bar 9 could be 8 eighth notes on the root - and a ninth eighth note would mark the downbeat of measure 10. Then the whole orchestra gives up a grunt ("huh!") on beat two of measure 10. Drum pick-ups return us to the last A...
Simply repeat A A B A until solos are done, repeat the melody and continue on to the "Coda" which consists of a tag (repeat the last 4 two times) - and then there's a series of 3 plagal resolutions (church style IV - I), and a ritard to the final I chord. Drums control the ending!