Here's what I've come up with.
1 Locking Nut
1 Nylon Spacer
1 Spring from a Pen or Mechanical Pencil
2 drops of Glue (I used E-6000)
And whatever you want to use for a Spinner Top. I'm thinking about using an old Duncan Imperial Yo-Yo I've had lying around forever.
I used a Dremel to cut away the mouse case. You could use anything that gets the job done though. A band saw, some sand paper, scraping it on the sidewalk repeatedly, your teeth, etc... Whatever works for you.
Drill a hole in your panel. Take the Bolt, add the Nylon Spacer followed next by a Washer. Put it through the panel hole and add the other washer then the Locking Nut. Tighten until it twists easily but doesn't have too much friction. Cut away a bit of the mouse case as well as the part where the horizontal encoder wheel shaft connects to the mouse case. Take the Pen/Pencil spring and put a drop of glue on one end of it and attach it to the end of the encoder wheel. Use the L-Bracket to mount it to your panel, make sure the Spring/Encoder Wheel Shaft line up with the end of the Bolt. This might take a few tries to get right. (use scrap wood) Once it's all lined up, add a Drop of Glue to the end of the Bolt and Spring. Finally, add whatever you want to use as a Top and have fun playing.
Make sure you change the Analog setting in whatever game you're wanting to play. If you make this spinner Left is Right and Right is Left.
Thanks again to Steve B. for helping me with that.
In MAME, you can press Tab while playing, and choose "Analog Controls". There's an option to reverse the x axis which should correct your problem.