As you have discovered, antibiotics are no longer considered the best treatment for chronic infections of the upper sinuses. Regular sinus rinses do not reach the upper sinuses, because of gravity, the Flip-Turn Sinus Flush defeats gravity.
http://www.medhelp.org/user_journals/show/2322
The Flip-Turn Sinus Flush is mildly risky, because you have to bend over to do it, preferably in a shower, but you can also do it outside on soft ground, or you can kneel down and lean over a bathtub with the shower running.
It might take a few flushes to shrink swollen passages to the upper sinuses.