Electronic – Sense vibrations in audible range

A real schematic would help!!

I don't think the crosstalk is something in your circuit, but rather is acoustic. The other drums act as microphones and pick up the vibrations of the drum you're playing. The only solution I see is to add antisound to the other drums' signal, but that requires that you have a very good idea of the amplitude and phase of the signal you want to cancel.

edit (re your comment)
If hitting a disconnected drum doesn't give you crosstalk, then it doesn't seem to be acoustic after all. I want to have a look at your wiring. The signal should be a high peak voltage (high dV/dt), followed by a quickly decaying sine (the drum's resonance). If the wires between drums and microcontroller are very long and very well coupled (like intertwined), with the high impedance you have this may cause minor crosstalk. Not so much from the resonance sine wave, but from the fast peak when you hit it. But this should only give a small "tick" sound, not the typical drum.
So how did you wire it up? Try to use separate wires for each drum.

Try these linear amplifiers made by Apex. They are designed specifically for ultrasound aplications.