I have discovered that the challenge I'm doing actually reads slightly differently than I'd thought, however. It only counts airports you travel TO or THROUGH. So airports you only depart from don't count at all. There goes the leg I had from JFK to IAD. That one is not actually an issue, since I needed to do that flight anyway. But it means that one other trip I have booked is more complicated than it needed to be since switching airports on the return doesn't help at all. It also means I need to book at least one more flight.
Damn the small print.