Time zone support if using the FTP protocol requires support for the SITE ZONE command - please verify with Network Solutions that they have enabled support for that command on their FTP server. If they do not support it, then you can also ask for SFTP access instead, as SFTP uses all UTC values (avoiding the time zone issue entirely).
Everything works when comparing directories by timestamp. The synchronization process simply seems to have a bug (as described in the first post). Should I report that here or at Voyager?