1. Create an FTP backup of the live WordPress site before any changes are made.
2. Login to PHP my admin on the live WordPress website and select your database name on the left, then click on export above, and then click the save as file type in the lower left and then click go and save this to your desktop.
3. Open the .SQL file from step #2 in a text editor and then search for "youroldsite.com" and replace all instances with "SANDBOXsite.com" and then save this .sql file again on your machine. and be sure not to include WWW or http:// in the text replacement
4. Create a new MySQL database on the SANDBOX server, login to PHPmyAdmin and click the import tab above and import your .sql file with the new URL from step #3
5. Update the wp-config.php file from the FTP backup in step #1 with the new database name, password, username, and database host.
6. Upload the FTP files to the SANDBOX and then visit the URL and all should be OK and you can smile, however you may need to reset permalinks.
The reason im saying all this is because I move hundreds and hundreds of these and although plugins can cuase some seriously weird issues like you have here
in my experience its the moving and changing of names that causes the issues and if done correctly WordPress should function as on the live site. Doing all those
other changes is a risk and does not sound right to me. So take it or leave it, but I would give it a shot. Also this does not involve using anything with Backup Buddy so disable that before starting this process on the live site.