As a pure mechanical guy I can construct a relay-switch based setup, but I fear it will fill the trunk.

No, the arduino sounds like the best bet. And Nicks comment are spot on.

To get perfect sync, use 2 encoders , or even good quality potmeters that measure the axle position of the wing-pivots.

If the idea of measuring acceleration in 2 dimensions is workable, you can even have the wing, if it's flexible enough, torque to have more or less downforce at each side. You could even go further, and do the same with the front spoiler.