It looks like it worked. I copied the scriptApproval.xml over to the production Jenkins and I found the approved methods listed there.
Will know for sure if it works when I start my first production build.
I just added a few lines of new code and tried it out on my test Jenkins. I had to execute a build 8 times to each time add a new method to the approved list. This procedure to add to script approval one method at a time is ludicrous and time consuming.