After a week of more driving... Haven't heard the honking once.
Thank you for all the help @
Tcoat . I guess it just needed some grease! Not sure if I can pinpoint exactly where of the three places I greased up really fixed it, but it seems to have solved the issue!
So thankful I don't need to take to the dealership where they'd drop the transmission, spend a lot of time investigating, and cost me a lot of money.