Cannot save SQL.bak via SSMS to NAS: System.Data.SqlClient.SqlError: Cannot open

We have a QNAP NAS that I need to run some SQL backups (.BAK) files to. I'm trying to use SSMS 2012 to do this, but I get this error:
System.Data.SqlClient.SqlError: Cannot open backup device

I tried giving NETWORK SERVICE full NTFS permissions...didn't work. I then tried giving EVERYONE full NTFS permissions, but still no joy. I read here that the  NT SERVICE\MSSQLSERVERservice should have rights, so I added DOMAIN\SqlServer$ with full NTFS permissions to the folder on the NAS, but again, no change. Where am I going wrong here? Much thanks.