Hi Sheldon,
What's the voltage at VLcd when you have good contrast? If the voltage is positive then you can drive it directly with the PIC using HPWM and a simple filter. It won't be that easy if the voltage is actually negative, which I suspect it is. But in that case you may look into replacing the mechanical pot with a SPI or I2C controlled potentiometer chip. I'd double check that the datasheet for the pot-chip regarding min/max voltage.

/Henrik.