Every SG I've heard gets that crunchy kind of tone. Try a Boss Metal Zone to get a better distortion.
Another fix would be to change out your pickups. The other guitar player in my band plays an SG, and he just got the EMG 81 and 85 put in (the pickups Zykk Wylde uses) and it improved his tone 100%.
Ok, pick-ups aren't a bad idea... but, if I were you I'd invest the money into a different amp. TUBE!!! I had the MG series with the SG, so I know where you are coming from. Once I got my tube amp, those problems went away. Best suggestion go to a local music store try a SG through a tube amp. Even a tube combo might do the trick.