Right now the full-planet demo server is in Germany and lives at [1]. A brief explanation is at [2]. I'm hopeful that the project will continue to improve with time and eventually end up being a real contender in the web maps space. I'm talking with folks about the potential for getting some more robust hosting options too which is very exciting.
For the moment though, Headway has some usability issues. It's missing ETAs, has no steps list for directions, or proper geocoding search results page, etc. I'm going to get to these issues with time, but please drop me a line if you're interested in helping out. Especially interested in help with web frontend, design, or internationalization. Development takes place on GitHub [3] and discussions tend to happen in the matrix room [4].