I know he won't be flying but I'd worry about my dad having issues in a foreign country because he used a diferent name so I could benefit.
You say you are a full time student. You have Columbus Day, Veterens Day, Thankgiving and X-MAS holidays for a quick trip down the coast or to the middle of the country and west. It will only take 1 day to get 3K.
You can get some studying done on the flights. Lots of people here do that.
I'm sure you can find a way to devote 1 day to get gold status if it means that much to you. If you study, it isn't even a wasted day.
These boards are filled with students who do this all the time.