Ok, so I ordered a new set of LaBella strings, they arrived today, and I fitted them... exactly the same problem. I've also looked up fret positions, and as far as I can tell with a tape measure, they are in the right positions. I also compared to another 24-fret bass I have (which plays nicely in tune), and the fret distances seem to be the same. I tried lowering the pickups as far as they would go, just to make sure that they weren't causing an issue, and it made no difference. Unfortunately with these strings, you can't fit them the other way round, the eyelets are different sizes and the larger one doesn't fit at the 'nut' end. This is bizarre, this bass seems to be defying the laws of physics. I'm torn between taking it to a tech or contacting the retailer.