To me, it sounds like the perfect defensive system - but they usually lack a fatal flaw - They believe the system so perfect that no-one would dare try anything. This has the unfortunate side effect of expecting the unexpected and planning for it - but the EXPECTED happening tends to throw them off for critical moments.
What would be my solution?
Boldness..... something so bold that no-one would dare think it possible, and shock them long enough to spirit her away.
Personally, I could see the MC here insinuating himself in to being one of the girls "consorts" in one of the religious ceremonies (I'm presuming this happens in front of everyone, like a show? lol) During the act, he could simply steal one of the guards weapons (who would expect that?) - hold it to the girl's throat and walk out with her.
Once the pair are out in the city, well, it becomes harder to track them, but the whole city will be on alert very quickly..... so what wouldn't the guards expect?
Again, personally - I'd hide in the MOST obvious spot - guards that are arrogant or in a state of panic, won't bother checking the most obvious place to hide - then, when they've past - out they hop on their merry way.
.... that could use some fine tuning though, this is just off the top of my head