I tried a number of different options and ended up with a main theme that used some wide intervals for interest. The tone was a general purpose driven tone with a delay on it from the Carbon Copy, synced as best I could with the beat. I had to stitch together a couple of takes to get it right, which was annoying as it wasn't actually that difficult, but oddly the one glitch you can hear (at about 0:37) was due to me making a very slight mistake on fretting a note! At 0:46 I switched to the bridge pickup to vary the sound somewhat.
All very straightforward in Reaper, just a little EQ tweaking and we're done: