I got as far as mod_fcgi, but I couldn't figure out how to write a mono program to integrate with it. Found some nice C examples, but nothing for mono. I still think it would be a hell of a great side project -- lots of power and expressiveness in F# that JS doesn't have.
I assume you're aware of http://www.mono-project.com/FastCGI? I suppose you could just implement the FastCGI spec yourself, it's a bit fiddly but not that complicated.
Of course, this assumes you have plenty of time to spend on such projects. ;-)