Before you go any further, are you 100% sure that you do not have a hair clog ABOVE the P-trap? The most common place for a hair clog in a bath vanity is on the hardware of the pop-up stopper. This assembly creates restriction and all kinds of places for hair to hang up. I typical can clear these clogs by removing the trap, the lever on the back of the tailpiece that controls the stopper, and the stopper. On most sinks this can be done without tools , and talks less than a minute once you do it a few times. Then it's a matter of pushing a wad of paper towels or a small washcloth down the drain assembly and pushing a really nasty wad of hair into a bucket. It's a gross job, but it's also quick and easy. You may be chasing a clog in the venting system that does not exist, while missing the fact that the tailpiece is totally clogged. Hey, have fun....... I used to love showing this nasty shit to my kids, since it typically happened in their bathroom. It got my dear daughter to the edge of puking a few times. Ah. the joys of being "Handy". Don't forget what Red Green says, "If the ladies don't find you to be handsome, they better find you to be handy"