You have to be a bit careful with figuring out what John Squire was doing, as he was a pretty handy guitar player even back then, to say the least. Absolutely jaw-dropping later. If you can hear a ghost note an octave down, there's every chance he actually played that note quietly an octave down. When he sounds messy, I'm pretty sure it's all completely intended and intentional. Although a few have said he might have used an Octavia, it definitely can't play an octave below the fundamental. Most of the time it's a struggle to get a clear octave above. I don't hear an Octavia or octave pedal. (The one we did have around the time was the Boss PS-2, which did play an octave down pretty well, but I definitely don't hear it on I Wanna Be Adored.)
Guessing you will have already found this out, but at the time, he was evidently using an Ibanez Tube Screamer and Dallas Arbiter Fuzz Face (I'm guessing silicon), sometimes one pushing the other, into Boss PH-2 and BF-2 phaser and flanger. I have been bitten this kind of setup for many years now, although for me fuzz was from a Colorsound Supa Tonebender (best imitated by Ram's Head Big Muff Pi in the Axe FX), and phasing and flanging from MXR Phase 90 and EH Deluxe Electric Mistress. Never covered I Wanna be Adored, but regularly play She Bangs the Drums, and Made of Stone, and they definitely work with that pedal setup. I've played the last of those a few times recently, and the Axe FX imitating my old pedal board and amp setup definitely nails the vibe. I'll have to go back and check if it's anything like the recorded sound!
As well as the drive/fuzz, most of this can be directly modelled in the Axe FX. Not sure if we have a PH-2 or BF-2. If we have the latter, I really ought to explore. Amazing pedal, but maybe a bit too flexible for me. John Squire definitely knew his way around it! If there are weird noises you can't make sense of, they may well have come from turning the feedback ("Res") up on the BF-2. It can do crazy stuff.
The recorded guitar is swamped in delay of course, and there may well be some "post" treatment in the recording. (I'm thinking Aphex Aural Exciter, which does amazing things to fuzz and flanger sounds, some used it for tracking back in 2" tape recording days).
Good luck with chasing it down. Amazing player in an amazing band, I wish I'd taken a little more notice at the time!
Liam