Although the circuit of shown so far as the liquid crystal panel's AC driver works well, I’m not too happy with the intrinsic non-linearity of the FET. Because of this, today I designed and tested an alternative, a bit more complex, but I believe more elegant design. In the circuit shown below, the LCP drive amplitude tracks linearly with the DAC’s output.
The non-inverting amplifier built around U1 approximately doubles the output of the DAC. This voltage is then presented to an H-bridge implemented by the analog switches in U2. The H-bridge produces a continuous biphasic train at a frequency given by the oscillator built around U3A and U3B. U4 doubles the +5V coming from the Raspberry Pi to power U1 and U2. The LCP is connected between the legs of the H-bridge.