It is indeed a freehub/cassette (see here:
http://tilmun.de/rbw/images/3058980.jpg ) with "hyperglide" gears. I'm amazed something is going in my favor on this bike (amazing how a "free" bike winds up costing a decent amount to bring back to life).
I think I'm going to go with a 12T per your suggestion.
Thanks for all your help! Now I'm off to go buy a chain tool and a whip.