You may get a more natural tone if you use a solid state amp instead of a tube amp. There's a bunch on the market these days, from Fender, Fishman and others. I use an old Roland KC-300 and get ok tone from a Nechville banjo with piezo pick ups on the bridge.
The Lace pickup is by design hum canceling, so you might be surprised at how it sounds pushed up against the head from the bottom side. It will require more amp gain because it's further from the strings but that's not a problem for most amps.
I personally dislike the concept of modeling, but you may find what you're looking for with the Tonedexter system. It's quite the rage in the amplified acoustic guitar world right now.
The idea is you have the Tonedexter pre learn the ideal sound of your instrument by using a mic and creating a "wavemap". You can then play your instrument live using a pickup and the Tonedexter uses your loaded wavemaps to re-create your studio-perfect acoustic tone.
Steve you could go completely midi for a sampled tone.I mess with that a bit.Very expensive though.My own samples never get off the ground, in comparison to ''factory presets'' on my roland or casio. As far as tube amps I always liked their coloration.They rattle and creak like a banjo when Carlos Santana fires his up. Yes my low tuned banjo makes some difficult fiddle tunes become easier and still be in the right key. I agree with Rudy on the Lace