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That would be a Deluxe Memory Boy.

And that song just sounds like overdrive/reverse reverb to me. Standard MBV tone. Knowing they also have a keyboardist, I think a lot of the effects you're hearing could be that too.

Keyboard makes sense... I love the sped up/slowed down leslie sound the keyboard gets. Now to find a reverse reverb after I just bought my Supermoon

It looks like he has stuff under the top pedals. Looks like he's using a tbp switcher. I imagine one of the DDs is where he gets the reverse effect.

The keyboardist is playing an organ tone on that song I believe.

Also, don't underestimate the ability of vibrato (bigsby) and swells to make things sound cool. :-)

I saw them on this tour. He played all jazzmasters, maybe a jaguar or two, changed guitars after every song.

Not only on this song but most of the songs on this record, the keyboards are designed to voice similarly to the guitar and on superficial listens, it is often difficult to tell the difference but upon closer listening, it becomes pretty obvious. Digiverb or Hardwire verb can definitely get the reverse reverb sounds.