Thanks, all (esp. BrianSlovakia, blonder, and Parobek82) for the helpful information. My paperwork was accepted by the consulate. I'll report back here when I have sense of the timetable. There's very little information in English on the simplified naturalization process, and I suspect this thread will be helpful to others, too.
For what it's worth, this thread has drifted quite a bit off-topic. Many of the recent posters are describing situations for which simplified naturalization would not be appropriate (e.g. children and grandchildren of living Hungarian citizens, citizenship based on residency, etc.). Please note that simplified naturalization provides an entirely different pathway to citizenship.