Through working with JIRA Cloud support, I learned that the only way to move a project from one instance to another, is to create a full backup, and import into the new instance. Then delete all of the projects in the new instance that did not need to transfer.
We use JIRA and Confluence for managing many different projects. Some of them have thousands of Issues, and some have been in use for over 10 years. When our support efforts were for a project that wanted to migrate to its own instance, we were stuck in a 2 month process of figuring out how to make that happen.
There should be more convenient functionality to move a project (Jira, Confluence, and any add-ons) between two cloud instances.