FOR LOGS:
Move-StorageGroupPath -identity SERVER\StorageGroup -LogFolderPath X:\PathToLogFiles -SystemFolderPath X:\SystemFolderPath
FOR DATABASES:
Move-DatabasePath Server\StorageGroup\MailboxStore -EDBFilePath X:\PathToDatabase
The problem was that we wanted to specifically use eseutil to move the databases. We used eseutil to push a good copy over, however, we couldn't repoint the database without Exchange trying to copy it over. I believe you can repoint the registry, but we opted to just trick Exchange in a manner of speaking. Due to size constraints, we created a new empty database, ran the above command to move it, then deleted the new database and replaced it with the eseutil copied one. This mounted up and worked great.
An alternative method to the normal methods of moving it over if you have odd circumstances to work under.