[mistwang]

I have set up a Fast CGI context called /cgi-bin/ which is linked to lsperld (this pretty much mirrors a Ruby on Rails setup (aside from the additional /dispatch.lsapi Static context) which does work).

that's the problem, you should remove that.
If you want to run script through lsperld, you cannot set script as CGI or FCGI context. have to define a script handler for certain suffix like ".pl". then just use static context to map to the directory holding the script if need.