Since running the wire during the middle of summer isn't an option, I made this replacement mount.  I believe it will work with minor changes for any cylindrical camera.  The trailer ball mount should be the same size for most vehicles.  

I've included the openSCAD file so you can modify to your heart's content.  It does rely on the threads.scad library https://www.thingiverse.com/thing:1686322 

Many thanks to all of you smart people out there making libraries for the rest of us.

I printed mine in PLA but ABS would probably work better outside.  So far it's lasted three weeks without any issues.  

Print each part as shown in the image and include supports on the build plate only.  The 3mm screw hole on the top should survive any deformation.

Hope this helps someone else.