I have this one figured out using an Arduino UNO and that GPS board. The limit switches inhibit the up & down relays from operating.
On powering up it is in automatic mode, all outputs are off and the GPS finds satellites and its position. When you accelerate to 62 MPH the spoiler goes up and stops when the limit switch turns off the up relay. When you decelerate to 42 MPH the spoiler goes down and stops when the limit switch turns off the down relay. This will continue unless you operate the dash switch, up or down. The limit switches inhibit that movement also. Once you operate the dash switch, it is in manual mode and will not raise or lower automatically again until you turn it off and back on.
BUT, the GPS takes 1 to 4 minutes to boot up, find satellites and its position.
It works fine with LEDs so my need to slay this Dragon is satisfied. If you still want it, you will have to persuade me to go buy relays, build a neat & orderly assembly on an Arduino prototype shield, build a test fixture from a sun roof motor with an arm and limit switches and drive around testing it to make sure it works as expected.
The circuit you showed last is good except that in the description of your spoiler, they say the limit switches are normally open and ground at the end of their stroke.
I would need confirmation on that point too.