That's a tough one. But, perhaps not impossible. While your group ride should have been more visible than an individual, it likely made the reactions worse as you nearly ran over each other.
Prevention:
Treat this like you're changing lanes or making a left hand turn. Look back to watch for traffic. Signal a left turn for changing lanes. Even slow down slightly so that you can take a partial radius before making the turn if necessary.
I've kind of made up my own signal, hopefully cars can get the gist of the idea. I'll point down at about a 45° angle to indicate (in my mind) that I'm moving left, but not planning to take the whole lane, or actually turning left (also do that around parked cars).
Reaction to the event:
Rather than slamming on the brake, I'd have taken a hard right hand turn and stayed with the car around the corner (and braked some). You could have even taken the full turn-off, and returned with the northbound traffic to get back on 14.
I'm usually riding alone, so a dynamic course change should be easy enough, but for a group ride, it might also have been safer than doing an emergency stop.