The SG getting you closest makes sense, since its humbuckers can give you a thicker, smoother sound than the Strat or Tele. With an AC15, I’d also experiment with lowering the gain slightly, keeping the mids fairly controlled, and using the guitar’s volume knob to clean up the tone rather than relying only on the amp settings. A little EQ and reverb adjustment after recording may help bring the recreation closer too.