Ok I spent a little time with it, I was actually curious about this one myself anyway.  I think I can offer a starting point or two, but you'll have to take it from there.  NYC apartments aren't kind to trying to replicate MBV guitars, so I did what I could with my Tele, a Space, an OCD or a Fulltone Ultimate Octave (only two distortions at my place right now), and tiny tiny 5 Watt 50 year old Supro practice amp.   I believe you can achieve something close his sound by using Space and a creamy overdrive or fuzz (neither of my two were quite getting me there).  

At first I thought he was using long reverb types and not playing too many notes, but after watching some videos, he appears to be strumming quite a bit on some openish looking chords (C formations and power chord looking stuff).   So, I think the reverbs are of the shorter reverse-reverb nature, b/c there is not any noticeable pick attack.  Also, I'm pretty sure the reverb has to go BEFORE the distortion, and you might even experiment with distortion on both sides of the reverb.  

Try this first (I'll give ranges b/c all guitars are different):  use the Reverse algorithm in Space, Tempo mode, Mix around 66, Decay 1/8, Size 50-70, Feedback <25, Low-LvL 50-75, Hi-lvl -50 to -75, Contour 30-50, ModLvl 10-30, Diffusion 40-70, Late dry 0-10.  

Strum a song like "To Here knows When" and tap in the tempo until it feels just right with all the swirliness.  If it's too big, pull down the standard late Reverb with Size or turn down the Feedback around the Reverse section (Delay know).  If you don't like the Mod, turn it off (I like a little b/c it's a good doubling effect, and the tracks on the record sound very layered to me).  You can add more attack at the beginning by turning the Mix down, at the end by turning Late Dry up, or in the swell up by turning down Diffusion.  You should also EQ to taste, but to my ears there isn't much piercing high end, I rolled it all off on my guitar and cut it significantly on Space, but this kind of stuff will differ b/t setups.  

You can also get good reverse sounds with BlackHole and MangledVerb.  In BlackHole use INV-GRAV on the decay knob, and in MangledVerb turn the decay to 60 or below.  In both of these, SIZE and DECAY will affect how long the swell lasts, but there is no Tempo swell.  Mangled Verb actually is a Reverb into a distortion, so it might get close…..I'd have to play with that one some more, you should try it.  

Also, I believe most of the detuning he does with his whammy bar.  I have no idea what distortions he was using.   The OCD flat didn't do it.  MangledVerb got close, the fuzz on the ultimate octave got closer.  I've read somewhere he used a RAT.  Do you know? 

-Russ