You can connect the LCDLED pin directly to ground to turn off the backlight, or you can connect it to a PWM output of the mega644 and achieve a variable brightness by rapidly turning it on and off. Lower current draw in exchange for lower brightness might be the only compromise you need to make.
If you want to power the backlight from a separate power source, you can cut the last two wires of the ribbon cable (the ones that correspond to LCD pins 15 and 16) and connect these to your regulator through an appropriate current-limiting resistor (the X2 uses 9.1 Ohms). If you still want to be able to use the LCDLED pin, you can just cut the ribbon cable wire that corresponds to the positive power voltage and connect this to the output of your regulator. If you do this, make sure your regulator and the X2 share a common ground.
Another option is to make a custom 14-pin LCD cable that doesn't connect the backlight pins to the X2.