FastCGI is about as old as mod_perl, but it works and you can use it today on the majority of ISPs. This is something we can thank Ruby and PHP for pushing. The bigger issue for you is going to be getting Perl6 onto ISPs. That will probably not happen until vendors start bundling it.
The thing about those C web servers is that most of them got going by cannibalizing an existing server, like Apache. Otherwise, the job would have been pretty daunting. It's not that people can't create a big new thing -- just look at Linux -- but they can't do it quickly from scratch with few people working on it. I think you'd be better off spending your energy elsewhere, since I don't see any real problem with the existing web server solutions. In fact, the only reason to write an HTTP server these days is if you have a real game-changing idea for it, e.g. the non-blocking I/O architecture that spawned the last crop of new servers.