I decided to remove one of the arm elements, and just stick with the shorter one of the two to test that out. The downside is: the shorter the arm, the less likely I am to get any selfie-style photos of anything other than a handlebar, tank, and pilot of the bike. I was hoping to see more of the bike, but that will require a different solution. The single arm setup is certainly more stable. But the amount of give in each ball, even with the knob clamped down as hard as I could get it, allowed too much movement with my DSLR attached to get a sharp photo, let alone be safe for the camera.
My conclusion for this is, the Ram Mounts camera mount didn’t work the way I was hoping it would, but with the understanding that I was asking a lot of this setup, given my camera with a medium lens weighs about 3.6 lbs. This setup would work great for a smaller camera, like a GoPro, or a small mirrorless camera. But I will need a secondary arm or a couple cinch straps to help stabilize this setup for a full size DSLR.