can you do this?
blue is a spring.
Red is a dowel (metal, plastic, wood, whatever)
orange is the shift lever, with the plunger in the middle
small green area is a smalll setscrew
shifter hole would be drilled a little long, so it goes past the hole where it will interface with the dowel, in order to create a small cavity above the button tube that a setscrew can align with, in order to allow a small setscrew to be screwed into the dowel after installation that will prevent the dowel from coming out of the ball... (savvy?)
if you use a metal tube for the dowel portion, a small square could be milled out of the bottom, where it hits the plunger, and an angled piece installed in the middle of the tube. this would make it easier to square the end of the dowel off, so it can mate with the spring. it would make it more difficult to drill and tap the setscrew piece though...
not sure if I can really convey that concept very well over text and a quick sketch in MS paint, but is this doable with the facilities you have? I saw your prototype with the button on top, and I figured if you can manage a top button that doesn't pop out, you could probably do a side one
EDIT: I forgot, you would also need a setscrew going in the side on the bottom, to secure it to the shift lever...