Yea I was going to suggest the 8 springs.
Just give the case box a large opening on the top for unrestricted movement and put some kind of a rubber / leather boot over it to clean it up.
One idea that I had about making a stick like yours was to have some kind of a ring with bearings that would slide down over the stick and position it to the lower portion of the stick and then somehow weld on many little hooks in a radial pattern around the outside of bearing ring, and weld the mounting hooks for the springs on the base plate in a circular pattern, all equidistant from the stick base.
That way you could have 32+ springs packed tightly together in an even radial pattern radiating from the bearing ring and the equal tension of the springs opposite each other on the base is what would hold the stick in the center.
The bearing ring in combination with the equal spacing of so many springs spaced equally apart would provide a near frictionless feel, and would allow the stick to move in any direction without and kind of X/Y axis uneven tension/clunk.
Not sure if that makes any sense or not, maybe I should have made a MS Paint drawing, lol.
I was bored, I had to draw it.

There's probably some blatant mechanical obstacle that would make it very hard to create that I didn't think about, but it seems like a good idea.
