Turns out my sinuses (sinii?) are fine; the problem is with my turbinates. If you know how to read the films, you can see that they're all swollen and that's what's causing my problems.
My ENT recommends turbinate reduction surgery -- which DS1 had last June, with great results -- but I don't have time to get it done before we leave for our vacation. It will have to wait until the fall, or possibly forever. It's an outpatient procedure and one that should contribute to my quality of life, but it's not strictly required, either.
For now I'm hanging in there on a course of Cipro, trying to get rid of the latest round of gunk. I'm hoping I'm not too miserable over the summer, but I'll manage somehow, regardless.