Finished this project and wanted to update. I removed the wheel and hub to inspect my work because the stabilitrack message wouldn't go away. After a closer look, I discovered that the washer was actually there from the factory. However, it was so small and much different than the washer I installed. It blended in and I barely noticed it the second time around.
The stabilitrack message was there because I installed the new washer on top of the old one which interfered with the readings.
Apparently the wimpy washer that GM used on my 2011 wasn't getting the job done so they began using a different part. The updated part number is below. The new washer is much more stout as you can see from the pics.
I removed the old washer, re-installed the new one and put it all back together. No error message and no clicking. Very happy. Now for the passenger side. The annoying clicking was there too. I took it apart, swapped out the old washer for the new one and no more clicking, finally. The noise was really annoying and I'm so glad my problem is solved. Passenger side was really quick and easy.
So, even if a Camaro has the washers from the factory, they can still experience the clicking. The updated part number for the improved washer is: 11611965
Pic 1 shows the axle with the washer installed from the factory. Pic 2 shows the axle with the new washer installed. Quite a difference.