I would guess that the two resistors to the right of the LCD, forming a voltage divider, are the contrast control.
If you want a cheap-ass seven-segment LCD you should get a calculator from the 1$ store. Many more digits and only $1!
I looked at hacking the harbor freight multimeter, but it appears to be an intergrated multimeter chip/display. One might consider using the rotary switch and resistor banks as an adapter for an arduino for converting voltages and resistances into something easy for the arduino to input.
The application notes for the chip give this list of LCD suppliers:...
I'd LIKE to be able to make a "Multimeter Shield" that you could use to adapt to any electrical value the meter could measure.