Hi Greg,
First, make a backup of both sites.
After making a backup, does your host have cPanel? If so, you can use cPanel's File Manager to move it over easily (similar to the first half of this tutorial:
www.ostraining.com/blog/joomla/move-a-jo...t-directory-to-live/ )
You'll want to create a new subfolder and move the root files and folders into the new subfolder (excluding the subfolder that you're wanting to move to the root and the host's folders), then move your "beta" folder's contents to the root folder.
That's about it. Then check your permalinks.
Let me know if you have any questions.
Kind regards,
Nick