I have watched two youtube videos that may be useful. An acoustic cover playing lots of extended chords and a piano cover with illuminated notes.
From the acoustic cover.
Intro and Chorus:
Emaj7 __ A#m7b5 __ Amaj7
Emaj7

A#m7b5
Amaj7
Verse:
Emaj7 ā Dmaj7
Emaj7 ā Cmaj7 ā D7
Emaj7

Dmaj7

Cmaj7

D7
Analysing those chords:
Amaj7, A#m7b5, Cmaj7, Dmaj7, D7, Emaj7
Written as reduced triads:
A, A#dim, C, D, E
Letās immediately see the A#dim as a chromatic passing chord and concentrate on the others. We then have the problem of four major chords in a progression. Or do we?
The verse and the chorus can be seen as separate progressions. The chorus is easiest, it bounces between an Emaj7 and an Amaj7 (with a passing A#dim). This could be in the key if E, boucing between I and IV chords (E and A respectively). Or it could be in the key of A, bouncing between V and I chords (E and A respectively). Given that the chorus spends more time on the Amaj7, and the chromatic diminished leads to it, I am more minded to go with it being the latter.
What of the Verse then? It has three major chords all two semitones apart. Emaj7 drops to Dmaj7 in the first half. Emaj7 drops to Cmaj7 in the second half. I do think it can be seen as being in the key of E major. E is prominent and feels like home. Both Dmaj7 and Cmaj7 feel like journeys away from the tonic. The riff too is based around the note E.
If we take E major as the key then Emaj7 = the I chord.
D maj7 = bVII
Cmaj7 = bVI
Both are borrowed chords.
Cmaj7 is borrowed from the parallel minor key of E minor.
Dmaj7 is not borrowed from there however.
In the key of E minor, an extended D major chord becomes D7 not Dmaj7. We have a brief appearance of a D7 so we have now explained it, but not the Dmaj7 - which is a right āpitaā.
There might be a temptation to look at a bVII and think we are in fact not in E major but in E mixolydian. But if it was in E mixolydian, the E chord would not be Emaj7 it would be E7 so that cannot be the case. It is possible, however, to view the Dmaj7 as a chord borrowed from E mixolydian.
To summarise:
Chorus:
Either
I ā IV in the key of E (Emaj7 ā Amaj7) with a chromatic passing diminished chord
or
V ā I in the key of A (Emaj7 ā Amaj7) with a chromatic passing diminished chord
Verse:
I ā bVII in the key of E (Emaj7 ā Dmaj7)
followed by
I ā bVI in the key of E (Emaj7 ā Cmaj7)
plus
a passing D7 borrowed from the parallel key of E minor.
This is a song best enjoyed with the ears, and the āsurpriseā that the borrowed chords bring, rather than providing a tasty theory snack. 
It does make me think that at some point my borrowed chord ramblings will migrate over to here.