These requirements seem pretty arbitrary. Is your server, which depends on perl, SSL libs, and a bunch of modules, really more "standalone" than Apache and some perl code? I suspect the real meaning is something like "must be easy to install and not have any licensing fees." There are some nice click-and-drool installers that will put Apache, mod_perl, and mod_ssl on a Windows machine, and you could add more to them.
Maybe I'm just overestimating the difficulty of writing a reliable HTTP server. If this is a controlled environment with specific client browsers, it may be easier than usual. You could look at some of the existing non-blocking servers like AxKit2 for help. I haven't seen a working SSL plugin for it though. There's also some POE stuff that I believe does work with SSL.
Is it really that important to use non-blocking I/O? There are simple, well-established techniques for handling long-running processes from CGI that can be used for most forking/threading situations. You essentially spawn a thread to handle the job and have it write progress updates somewhere that you can grab them for display.