I had a similar challenge, but without backlight. I programmed the hardware PWM to be a squeare wave oscillator at around 10 KHz. I then used two shotky diodes and two caps to double the voltage. After an LDO 5 volt regulator, I had enough power to run the LCD. Hopefully the backlight you chose can be powered seperately from 3 volts. If not, you will need a real boost regulator (try Maxim) to give you enough current for the backlight.

Ron