In the SiteSpinner Publisher window, click the "Browse" button. Do you still get the error? If so, try changing the connection mode from FTP to FTPS. Also, if your host uses SFTP for file transfer, SiteSpinner does not support that mode.
Not sure what you mean by your "separate pages" vs "project" statement. I assume you used the "files on disk" option to get your project published so you can upload the pages to your site via Filezilla. When you use this option, what you get is an exact duplicate of what would be on your site's root folder had you published via the FTP/FTPS option.
If you are using the "local" disk option, and find yourself publishing one page at a time vs publishing the whole project at once, go to the "Pages" tab in the publisher window, and make sure the "Export all pages" option is active.