I only used the clips about 4 times, then changed to a mountain bike as I sort of damaged my normal bikes wheels by jumping of a quite big kerb near where I used to live.
The trick I found was to try an anticipate when you are going to break, and then as I was left footed - as soon as my left foot was at the bottom of the cycle, remove it and then come to a stop.
Most of the riding was down a bridled cyclepath though, so there was very little vehicle interaction.