Why not install Apache, and set the file to transfer in the http-doc directory then kill Apache when you don't need to transfer a file? Unless you want to get fancy, you can have Apache running on whichever machine is sending out the file. That is a simple, but pretty ugly solution.

If HTTP gets through, that means port 80 is open, right? Why not just set up a FTP daemon (only when you want to send or receive a file) that listens on port 80?