After trying a million combinations, I finally figured out how to export data in SSIS using an OLE DB source (SQL Server) and a flat file destination. In the end all I really should have done was use "ENCODING UTF16" in the COPY command in Redshift. None of the settings I changed in SSIS actually helped, aside from making sure the Unicode box was checked in the General tab of the Flat File Destination settings.
select 'ALTER DATABASE [' + name + '] SET QUERY_STORE = ON ALTER DATABASE [' + name + '] SET AUTOMATIC_TUNING ( FORCE_LAST_GOOD_PLAN = ON )'
from sys.databases
where name not in ('master','model','msdb','tempdb')