If you are willing to lose GPS, maybe you could set the car's internal clock to the year 2000. This might fool a cursory data dump that is looking for "last three months of driving habits". Would obviously not stand up to any real scrutiny, but mostly painless.
GPS provides the time, so this probably won't work. If it ever reconnects it will just reset its clock. That's often one of the first things that any computer does after a long period of no power/connection.