To deploy a new version of our website we do the following:
I would suggest keeping the old files there and simply overwriting them. That way the downtime is limited to single-file overwrite times and there is only ever one file missing at a time.
Not sure this helps in a "web application" though (i think you are saying that's what you're using), which is why we always use "web sites". Also with "web sites" deploying doesn't restart your site and drop all the user sessions.