A computer mishap put me offline for a week, and prevented me from reinstalling my flight sim and new joystick. I'd forgotten that I hadn't posted the results here.
I ended up getting another Thrustmaster, the Fox 2 Pro USB, which a friend recommended. It cost less than I expected to have to pay, and so far my only complaint is that it looks rather anachronistic controlling a World War I flight sim.
I would recommend Red Baron 2, if it were still on the market. When I went looking for patches for it, I discovered that it had quite an active mod community.
Most of the recommendations I got from threads like this one were for Logitech, Gravis, or Saitek, but all of those models that I looked at reviews for were about half positive and half negative. The Thrustmaster's reviews were about 80% positive.