Andy,
Both tables are in SQL Server 2005.. different servers. However I did find a way to fix the problem...
In SSIS I went to Tools > Database Tools > Table and Database Designers > Column Options
In the drop down "Default column type" change to "varchar".
That fixed SSIS's conversion of the data to nvarchar.
However if I ever have to go from a nvarchar to varchar.. I guess one of the ways you listed is the way to go.
Oh, I have made it down to Level 5... Very good article and easy to follow.