"...I'm assuming there has to be a way to get around whatever mechanism is blocking the auger from accessing the lower areas of the pipe..."
No. The mechanism blocking the auger is the part that actually keeps the water in the tub when the drain is closed and is connected to the other end of the rod. They come out together. The other end of the rod where it connects to the stopper mechanism has some play and is much smaller than the overflow so you can get enough of an angle on it to pull the rod up and out with the stopper on it. If you cannot, you have some other problem going on and you will probably want to call a plumber.
Do NOT use drain cleaning chemicals like Draino and Liquid Plumber.