What I noticed from the videos is that you're using a LOT of brake coming to corner entries.
Slow in, fast out is good, but you have to keep the car settled too. Using so much brake that you actually hear tire squeal in a straight line will upset the car through the entire corner. Smooth is the word.
I try to stay off the brakes as much as possible during a run, and only brake in a straight line, and only just enough to set the front for entry into the turn.
Also Jason, you said that you've really not done much as far as setup on the car. A good alignment and experimenting with tire pressures will go a long way in making the car feel more comfortable and predictable. Your M3 is a good piece, but every car needs to be optimized to perform. How they roll off the show room floor isn't the way it needs to be to be fast through the cones.