I cut out some time spent in the menu as I spent extra time. As you can see, even if I had managed to pull the driver out, it still wouldn't be faster. It's not far behind though and does remove all of the BS you might face with the normal taxi warp. Also, it gives you an idea of just how easily you can fail to enter the taxi when you're dealing with high FPS.

• Kyle

This works both during and out of the mission. The taxi will not despawn when you touch the marker.