I do stand by the 8-bit resolution being sufficient, though. My idea is to determine at what point the wave peaks, thus allowing me to be able to compare the peak of the square wave that created the sound to the peak of the corresponding sine wave in the receiver.
I've looked at the transducer receiver output on an oscilloscope, and it's a clean, symmetric sine wave, so I was thinking that I may even be able to deal with a lower sampling resolution (say 400kHz instead of 3MHz) if I could reconstruct the sine wave in code and calculate the location of the peak.