The first thing you should do is ask about making a nice case on a specialized DIY Arcade forum. They're experienced with this kind of project there. Simply make the stick Amiga only, and use a ready made converter, like the cable suggested above.
Another option is to buy a good, ready to use arcade joystick, rip out the electronics, and mod it to connect to the Amiga. Good ones can be pricey, though.
It would be interesting to try a new model of joystick ergonomics. Maybe a flattened cube shape with a single switch on each vertical facet (up, down, left, right). The top might have 2 fire buttons.
OR
Start with the same box and use industrial spring loaded toggles - one for up/down the other for left/right. The switches could be installed, again on different faces, with the plane of toggling naturally oriented to the direction they serve. This could be a very intuitive and responsive controller. Might look kind of like a steam-punk design.
Fun to think about.
Yeah, I'm sure that's a whole lot easier and more intuitive than a joystick, where you just move the stick in the desired direction :rolleyes: