I'm going to disagree with all of you, but this has always worked for me. I barrel race and for me and most of my friends, the best way to sink deep in the saddle and keep those heels down is longer stirrups. I'm not kidding. I have always ridden with long stirrups and it has caused me to keep my heels down because when they slip up, I lose my stirrups. Whenever I have shorter stirrups, my heels flip up because I don't have to stretch down, and I then usually drop them. As long as you have a deep seat, you will have deep heels.
Hope that didn't sound too out of wack, haha.