I started with 150 grit dry sandpaper and removed most of the clearcoat finish.
I then used wet sandpaper of progressively finer grit to get a really smooth finish; first 220 then 800 and finally 2000.
The final uncoated finish looked like this.
I then sprayed it with multiple layers of clearcoat from a can (Autozone).
I added a cool decal to the back side after 4 coats were applied. It took some experimenting to get the right coating coverage. Initially I went too light and the surface had that orange peel effect. I went heavier on subsequent coats until it began to run. Light sanding between every 3 or 4 coats made the finish smooth. Finally, I finished it with rubbing compound and car wax.
I need to borrow a neighbor's buffer to get an even better shine. It took longer than I expected but was inexpensive to do and well worth it. Wow, this almost beat flying!