Perhaps if there were a set of rules, they might be unenforceable and some cases would still slip through the cracks. But at least if there were guidelines defined by some sort of official international governance - we might have a fighting chance.

Please share your thoughts and opinions on this topic. What would these rules/guidelines look like? Who might we lobby to enact such a thing?

My suggestion would be to focus on what you have proposed without the "official international governance" part. What seems to be lacking is a best practices document that describes the optimal way for the powers-that-be to enact time zone changes. Such a document could explain which communities should be advised or consulted in enacting such a change, and the recommended amount of lead times that different industries need for changes to propagate. It could also describe potential risks (such as economic impacts) of making such changes, particularly with a short lead time.

If such a best practices document existed, that would be a good foundation that one could use to pursue awareness with the relevant governing agencies. Jumping straight to official governance route seems to me to less likely to achieve anything. In my experience, governments are generally quite eager to have practical documents developed by experts that they can use to help guide them. They do not have to have to be enforced by treaty to have utility.