the less is more thing with gain also comes into play when you start compressing. Parallel compression will get you closer to your beefiness. Try a compressor that's going to give you some harmonic content. Look at softube for that.
Maybe try a few distortion pedals in front of your simulation. Nothing over the top, maybe a tubescreamer set below 12 o'clock.
Just remember to keep it in context with "the mix."