Took the car to the local radio control hobby shop. They played with the steering mechanism and told me that it was "all bound up". The ball joints had ceased within their plastic housing. (I got the car as a freebe.) The solution was new tie rods. (Fashioned out of two bits of plastic, tiny metal ball joints and #4-40 screws with their heads cut off. It took the guy behind the counter no more than five minutes.)

Now the thing steers like mad. Gotta calm it down a bit.

Ken