I found this square wrench. It is branded by Yamaha.
I started widening two sides to make the gap 1/4" and then made two grooves in the other two sides to make hex bits fit in. A few delicate finishing touches with a hex bit and a hammer, and the bit driver is done.
I was thinking of gluing a tiny magnet at the bottom, but the bits are tight enough.
It is amazingly comfortable to use. And the amount of torque you can exert is ridiculous. It even has a hole for a keyring!