Hi,
I have fast labours also... the first I thought was a fluke. Under two hours from the first contraction, made it to the hospital but was a HORRIBLE car ride. THis labour began with double peaked contractions 2 minutes apart and was fast and furious was in transition after a few contractions
THe second baby the doctor told me to get ready to deliver at home or on side of the road. I thought my fast labour was a fluke, but I took his advice and had towels and blankets in the car and towels and blankets at home. When labour began it was softer and slower but I rang the hospital and said I was coming they LAUGHED at me as I had only had two contractions when I rang. 50 Minutes after my FIRST contraction I was holding my daughter, I had my head down on the floor of the car and my bottom up trying to stop her coming out in the car, it was uncomfortable and stressful, despite having the towels etc in the car my partner did not want to stop!!!!
When the doctor arrived well after the baby was born, he said that I dilate without any contractions so when it's labour time, I have a few contractions transition and then baby.
When I got pregnant with my last daughter, I knew for certain that I did not want to ever have a car ride in pushing labour like that. I hired a homebirth midwife who lived an hour and a half from my place. She was so supportive and helped me have everything in place to be ready to quickly deliver my third baby. We had some plans in place to slow down the labour so that she might make it and so that I did not go into shock like I did the last two births. So when I went into labour I stayed laying down for as long as I could, my partner quickly filled the pool, and I began the holding on until midwife arrives!! We rang her whilst I was having my first contraction, i stayed in bed, I felt the pressure within a few contractions, and all the typical transition signs. I got into the water and again I was holding on, but nothing like the first two labours. Midwife arrived, I asked if I could push and she said I already had been!!! Baby arrived 2 hours after first contraction, my longest yet with the help of water and laying down!!!! It was a beautiful "slow" birth and I thoroughly enjoyed it!!! THe flip side to these quick labours is the afterpain, that lasts for up to three days and is more intense because of how quickly the baby comes out!

Whatever you chose be prepared, stay close to home perhaps? Personally I would stay home and ring the ambo's it's full on being in the car in that state and stressful for your partner too...

Goodluck with the birth, feel free to ask me any questions!!!