A good trick for piezo ceramics is to wind the transformer such that the fixed transducer capacitence resonates with the secondary inductance, probably at somewhere just lightly above whatever resonant mode you are trying to use, then a series R-L-C resonance somewhere below the mecanical resonance and you can get somewhere close to an octave out of a ceramic transducer (in water, in air the Q goes way high), you do tend to find that most of the power goes into that resistor however.
Measure the admittance/susceptance curves for your device in whatever operating conditions are normal (If underwater, don't forget to wipe the bubbles off first it actually makes a measurable difference), then you can calculate the device equvalent model and for there a day playing with spice is time well spent.
Most piezo ceramic devices for underwater service would laugh at 12V drive, a few hundered volts to a few KV is more like it, but 106dB@1m is also at least 100dB off the pace for serious underwater work so it may be that you are working small distance in air in which case 12V may be ok, but you will really struggle with bandwidth.
Given your operating range there is no reason not to use a squarewave drive, consider the harmonic series of a squarewave the first non zero harmonic is the third, which is outside your intended bandwidth, and a mosfet H bridge is MUCH more efficient then a linear amp.
My hunch is that you have completely the wrong device for a chirped system in air.
Regards, Dan (Who used to do sonar transducers to pay the bills).