OMG, that was so very nearly my story too!
I haven't had time to write it up yet, but my water broke at home, we pulled away from our house at 4:48 am (the doula timed it when we called her) and drove to the birth centre (usually a 40 minute drive) VERY FAST. Her time of birth was 5:15 am. I started pushing the second I got into the centre, and she was out in two pushes.
I'm so glad everyone was safe and healthy!