Heck i'll give it a shot (i got prime lol) .. it seems to downgrade the unit to make it less secure and that is I guess what is preventing my older car from linking with the newer garage system. I am not sure why you are unable to sync yours though, the purple learn system should work for your car especially since you were able to program a 3rd party remote to your garage. Have you tried programming it to your other buttons on your homelink... i've seen some just not work on a particular button and people have had to go with their middle or right button.
well, guess what? Maybe the solar eclipse changed the mater around my place, but today I decided to give the programing another try. And it works! Held remote next to mirror, pushed in and held remote button, pushed in and held mirror button until it flashed for sever seconds, and when it stopped fhashing I let go of both buttons and then pushed on the learn button on my garage door opener. Went back to the car and pushed on the same button I had programed with the remote and the garage door light flashed. I pushed on the mirror button again and it closed the door! Wow.