OK, although I've never tried gettin that tone from an SG....mabey this will get you closer;
- Find yourself a compressor, and MXR Dynacomp works well, other guys have luck with a Boss CS-3. The Boss seems more readily available and has a Tone pot so you can brighten your tone a bit. The Comp is used to even out the attack and to "squish" the tone...in a good way. I use a Virtual Sound Rt 66.
- Use a Hybrid Picking tecnique. Use your fingers on the High strings to SNAP the strings against the frets instead of plucking,this is key to the Tele/ChickinPickin sound.
- Dial out some Midrange on your amp. Alot of Tele players,myself included, use Fender Deluxe Reverb and Twin Reverb Amps. The Deluxe has no midrange control and this paired with a Tele, gets a twangy/wiry sound, especially on the bass strings. Remember, you're playing an SG so you have wayyyy more mids than a Tele to begin with. Keep that in mind. Mabey use an EQ pedal for a preset Tele'esque tone.
- CHANGE YOUR STRINGS!!!! KEEP EM' FRESH!!!! The sound of new ,un-crudded strings will not only twang better, your intonation will be better and they'll play easier
I'm only on one cup of coffee so far today so thats all I can think of so far.
Good Luck,
Ian