Interesting take on the use of the pickup. Never would have thought of that. That would be an excellent choice if you're looking to harmonize but not have a drastic change. You'll get a mild tweak on fullness (depending on your pickups) compared to the very full sound you get when using the octave method. Comparatively i used a different octave plus the other pickup to see how that would feel too.
Alright so now i'm a bit confused though. You're talking about a melody being a 3rd or 6th higher. How do I know which octaves are X higher/lower than the other one? When I harmonized my melody I just chose a spot where it would be easy to play.