Ok, guys, I had a professional come look at my system. He confirmed a few things:
(1) It's definitely not the air vent. My air vent is fine.
(2) I have a unique kind of clog. He called it organic clog. It's like a membrane. A snake will go right through and everything seems fine. But as soon as you pull the snake out, the membrane closes itself back up.
He told me the only thing I can do is keep pouring strong acid down there until all of it is dissolved. And he didn't even charge me a cent.
Looks like I'll be pouring acid down there for the rest of the day.