All right, I decided to give this Tonematching thing a go and see if it's really as good as it sounds. My experience with Fishman Aura left me completely disenchanted with trying to get some good acoustic tones out of my piezo-equipped guitar.
So! The best advice I got on this was to select a mono input. LEFT ONLY on the USB input. That made a HUGE difference and got rid of the hollow phase issues so typical of the Fishman. Then it took only 2 minutes.
I used "Blue Moon" on Tommy Emmanuel's Acoustic album and went for it. I can't play the tune so I just fiddled with some chords from Autumn Leaves and other things. But the tone is what counts: