We had one of these, it was specially designed for use in car seats and buggys. It had a little slit in the back that you pushed the buckle through from the bottom, and then the buckle went between the legs and then up through the zip gap. then you clipped the buckle together with the straps. It was a bit fiddly to do and our dd would usually wake up, but then as you say in the car they go back to sleep again pretty quickly especially at that time of night.
So if you are desperate and don't mind you could cut a hole in the back of yours and hem it.
It did work really well, because dd was very happy and cosy and putting her in the cot at the other end of the journey was much easier. Although you do have to keep an eye on the temperature in the car so that they don't get too warm.