I started with two samples of Spoonflower's custom printed wallpaper, each sample was just a bit larger than the back of the wheel, so there was plenty extra space to play with getting the perfect placement of the print.
I began by trimming the wallpaper sheet, cutting it down to about 1/2 inch wider on all sides than the wheel, and then carefully trimming a few holes in the back where there are metal bits that poke out from the back (to make sure that the wallpaper would lay flat when applied, and keep it from sticking to those moving parts.) I cut the holes just large enough to fit around the metal bits, and trimmed them to their final size later, so that I would have a bit of wiggle room in the application. Then I took a bit of painter's tape and covered all the metal bits and moving parts to protect them from the wallpaper glue. Following the directions I wet and applied the wallpaper, and let it dry for a full 24 hours. I also applied wallpaper to the front of the wheel similarly, pre-cuttung the inner circle for the wheel to the desired size and cutting it just a bit wider than the accelerator wheel (this application was a bit trickier than the back to be able to slide it in between the two wheels without making a mess. I also added a few randomly sized circles on the front side.
When it was fully dry, using a very sharp razor blade, I trimmed off all the extra paper. Then put on about 4 thin layers of semi-gloss(since the wheel finish already had a bit of a semi-gloss finish to it) modge podge , letting each layer dry 12 hours before adding the next. Then removed the painter's tape after everything had fully dried.
The spoonflower wallpaper is supposed to be easily removable, so I figured that the modge podge would help keep it from peeling off spontaneously, and should also prevent any scuff marks or discolorations. (whenever I stick the wheel in a bag for travel)
I'm pretty happy with the results, and so far I haven't had any issues with it wearing or causing any problems with spinning.