I know the song of course, but I deliberately didn't listen to it while I was trying to find something to play over this, so that I didn't get unduly influenced. A clean-ish tone seemed appropriate to go with the strummed chords, and to start with I tried D major pentatonic (which in my head is the same as Bm pentatonic), then I tried it again with a capo the 7th fret on to see if I could get some interesting open notes contrasting with higher notes. Unfortunately nothing was working and nothing sounded fluent, so I left it for a few days.
When I came back to it, I thought I'd try something different. In fact, everything different. Instead of a clean tone, I went for the scuzziest, messiest sound I could (courtesy of a Fredric Effects Unpleasant Companion); instead of playing up the neck, I just used the bottom string (tuned down to D); and instead of trying to make a solo out of it, I tried to make a riff. I think I had something White Stripes-y in my head. Once it was done, I added the same notes in again, two octaves up for a bit of contrast.
With this kind of sound, the guitar doesn't matter as much, but what I had in hand at the time was the Yamaha SA2200. It was recorded dry; I tried adding some reverb or delay in Reaper, but the sound is so filled out that it swamps anything subtle. I settled for a bit of EQ to take the bottom and top ends out and emphasise the mids. What we have isn't brilliant, I don't think, but at least it's a bit different!