So far I haven't found a way to do this for free, but Panics Transmit FTP client has a feature that can mount FTP, SFTP, Amazon S3 and WebDAV servers as real volumes in OS X Finder. The feature is called Transmit Disk.
This site is static. That means I publish it in a local folder on my Mac and then upload it to the server. The upload is automatic. Transmit Disk has mounted the server as a volume. I then have Noodlesofts Hazel monitoring my local folder for changes. When it detects a change it immediately syncs the new or changed files to the server volume. It usually takes a couple of seconds.
You don't need Hazel to do the syncing. There are apps that only handles file and folder syncs (Hazel does many other things as well). One is FolderWatch by Brothers Roloff.
There is a trial version of Transmit on the website.