Didn't you ask this on another forum? Or didn't you like the answers you got.

Anyway, here's mine again.

Based on a similar application not involving a bike.

Start by drilling a hole of the right diameter in the right place* to form the end of the slot. Use a coping saw, or hack saw to connect the current slot's end to the hole top and bottom, slightly narrower than desired (how close you work depends on your skill and confidence in sawing to a line). Finish by filing the slot to final dimension.

* the location of the hole is critical because it's important that the dropout slots are parallel and at the same height. Otherwise your rear wheel won't be vertical. Don't measure twice, measure 3-4 times and be sure. If you're not sure of the accuracy of your measurements you can file the top of the slot on the lower side using a wheel you know to be true and dished correctly to check until it's exact. later you'll have to remember to always install the wheel on the ground, so gravity ensures that the top of the slot rests on the axle.