This strikes me as the kind of thing we'd need a full programme item to do justice to - in the same vein as "Man of Iron".
Get yourself a slot and a room, advertise for principal singers, give each one a rudimentary bit of costume to get in character (yes, you can use my Gandalf hat) and print out sing-along sheets for the audience. For extra credit, get an OHP with a still from the movies to provide backdrop to each scene.