The fact we're having this conversation leads me to believe the BTL would be a great candidate for your application. LOL
I ran my BTL in a 5 cu. ft. tuned to 32hz. Going with the largest recommended size will net the smoothest response. I did the minimum of 16 sq. in. per cubic foot, and still ended up at 6.3 ft.³ internal volume. So be prepared for a really large enclosure.
The BTL treated me good on just about every kind of music. I had a sub woofer level control on the head unit, and just set the sub to sound musical at zero. When I wanted things to get violent, the knob got turned!! That is when the BTL really shined and pulled away from the pack on the low end.
As far as a second battery. I would recommend going one of two ways. Either set up everything else and see how your voltage is... or if you have the money to invest just drop it in and be done with it. Too much power is definitely better than not enough, on so many levels. I had a 250 amp alternator, a 3400 under the hood and a 1200 in the back, and the headlights still dimmed at full tilt. But it was oh so heavenly being bathed in bass when needed.
My current set up is two 15" Icons in a sealed box. I think any less than that after the BTL and I would not be satisfied. Hope that helps in your decision.