SQL Server to XML files alternatives
Your current setup seems to be on the right track. I would cut SSIS out of the equation - the stored procedure INSERTs into the staging table, and then a C# app pulls the data out, creates the XML files, and SFTPs the files off to the destination. I realize that's more a 'developer' solution than an 'DBA' solution, but flat files and SFTP are not things well-suited to SQL environments.