Hi Longpole,

You can't switch the negative voltage without a voltage translator. It is approximately -10v below the pic ground vss.
Think of the contrast pot as a simple voltage divider connected between +5v and -10v or 15v total.

Using a pnp and pwm you can adjust the positive node of the voltage divider up or down by 5 volts. This in turn moves the center point of the voltage divider (Vlcd) up or down. It can be in negative voltage range as long as the pot is adjusted towords the -10v end. So in theory it should control the contrast. Hope you can make it work.