Nobody else out there has built a stand-alone arcade stick instead of a cabinet?
How complicated can it be?
Four bits of wood around 4-5 inches wide, arranged into a box.
Top piece a little larger, rounded corners, use a router to do T-molding slots.
Use some blocking pieces inside/under the top piece, to screw down securely with nothing visible outside.
Bottom piece is just scrap piece to cover the bits, screw it in directly.
Suggest you use smaller-but-decent joysticks like Sanwa.
There are plenty of cheap encoders out there these days.
If you want two-players, make a second box. Then you'll get more elbow room

Or just buy something like what pbj linked.
Really can be whatever you want.
Have seen people do it with those plastic storage boxes. I've made a control panel out of a plastic lunchbox before.

I've also got a control panel box with no T-molding, which I prefer. I don't much like T-molding on control panels, least not at the front of a flat panel (can cut into your wrists). Hacked gamepad inside, USB connect.