I don't know how well it would work for your game, but I've heard that some interactive fiction writers give away the game itself (maybe to get it out there, maybe because it would be impossible to prevent piracy). They then create and sell "feelies", which are little trinkets that add to the game experience or may even be necessary to complete the game itself.

It sounds like a reasonable approach. I do have a friend who makes an online TV show that he dishes out for free, and he manages to make a fair bit of dough by selling related merchandise (t-shirts, toys, etc.).

Two caveats though: I didn't hear how effective they are at selling feelies, and feelies have been a part of interactive fiction game culture since the days of Infocom (which may bias their customers towards buying feelies).