Radley: Did you ever try an external distortion unit, like Mi Audio Crunch Box or Suhr Riot or similar, with a clean preset? The feeling of that combintation is so real! I love how Crunch Box or Riot combine with the stock 'Sultan' preset.
Maybe you should 'unload' your guitars pickups with any external booster/EQ/something like that to make the combination of guitar, cable and input analogue again? Try some stomps when you have them lying around, maybe that the trick for you?