Ideally, what I really want is to move all of the content, and delete the mistake place & group. Is that possible? Will there be unintended data loss?
Yes, you should be able to accomplish a bulk move of the content. If you are using Jive Cloud then the "bulk manage content" feature (Using the Bulk Manage Content Feature ) accessible via the space's/group's manage menu should allow you the option to move over content.
Or, if you are using an on-prem/hosted version of Jive, then the Curate Tool FAQ should provide a similar functionality through an add-on.