I got an e-mail from Roddy that I should check out his forums. Well, I'd been there before and thought I wouldn't find anything new, but behold: a thread on Squabble, Chinese Scrabble. You play characters by combining cards with the right radicals, and you can steal peple's characters by adding radicals to an already formed character. At US$ 30, it's a little expensive (plus US$ 15 for shipping from Taiwan). But if you can get your school to order it, more power to you. Maybe I can get a grant from the Center.
Also, it's worth browsing Roddy's main site, which is chock full of practical information and anecdotes about living in China.