IIRC, your just going to have to move everything manually. FTP all your content over, dump the MySQL databases into the SQL server on the H-Sphere cluster. Migrate all the mail over (You can just set up your mail client for both new and old accounts at the same time and drag the messages across).
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If you have root access and a large number of files there are ways to do imports. If you are talking only a few sites I would ask the new hosts if they could ftp your files at the server and if you could get ssh access to quickly import the mysql databases.