There is a topic here that really needs to be discussed and that is scale length. The SG (and most Gibsons) use a 24.75" scale length. Telecasters and Stratocasters use a 25.5" scale length. The longer scale/string length of the Fender requires a higher string tension to get the same notes. This is a MAJOR factor of what gives Fender their clarity compared to Gibsons. You will never get this sound out of your SG. When I read the OP, the first thing I though of was P-90's until I read that you tried and didn't care for them. I am willing to bet that the P-90's you tried were in a Gibson and not a Fender. I believe the guitar you are looking for is a Telecaster with P-90's. I built a Telecaster with GFS Mean 90's and it is one of my favorites for the reasons you mention. The Mean 90's have a Humbucker form factor so if I ever wanted to swap them out with Humbuckers, I could. Look for a MIM or Squier Tele that has humbuckers and swap them out with P-90's. (While your at it, upgrade the jack, pots, and switches if you are able). The GFS Mean 90's have a very good reputation on this forum.