So it's become apparent that trying to suppress all of the different update prompt mechanisms that Oracle is using will be an ongoing, trial and error battle... until they change things. Previously, the script was unchecking the "Check for Updates" option and removing the Launch Agent that checks for updates periodically. However, if you were still on an older version of the plugin, it would prompt to update when you opened a Java app.
I updated the script now to add some more keys to the deployment.properties file. This appears to suppress the update prompt when opening a Java app. The keys use a version specific number, so I'm grabbing that number from a file within the plugin and using as a variable... hopefully allowing us to be able to continue using the script every time we roll out a new version of Java. Unfortunately, we have to run the script after every Java update. Hopefully Oracle will give us some better options for controlling this in the future.
Let me know if anyone has any better ideas, or ways to improve on this way of doing it. Any time I update/modify the script, I'm editing the previous versions on this thread in case people grab those copies. For the updated version that also suppresses the prompt when using an app, see either of the previous posts containing the script.