Get a driver like this, then make an adaptor out of stacked washers to your desired height, glue or tape them together. Then, put your screw inside the roll of stacked washers, and when the driver hits the washers, it'll stop at your desired depth. You'll want your washers to be big enough for the screw to fit through the center hole, and the bit to hit the washer face.
Only drawback would be you couldn't do screws any closer together than the washer wall thickness. You may need to just hand drive some between the ones you use the washer and bit with.