After drilling the three holes, get out your assortment of tiny screws. We'll want three that are the perfect size, height and girth. Also the flatness and the size of the head of the screw is very important.

Carefully thread the screws you think would be best into the holes you drilled. Remember you are creating latches using these screws. Do not screw them in all the way, that would defeat the purpose. Screw them in halfway or so, allowing the battery door to latch under the screw head.

The second picture shows the screws I chose.