Though the logline is a bit long, it's an interesting idea. I don't quite understand why they would age when they land on Earth.
If you allow me to brainstorm a little.
The aliens monitor transmissions from Earth, on their home planet, which is maybe 60 lightyears from Earth. They discover that some radio signals contains video, i.e. TV.
Radio signals travel at the speed of light. So a planet that is 60 lightyears from Earth would pick up TV shows that were transmitted in the 1950s.
The aliens finds that one TV show they fall in love with it. They pick up the manerisms and speech patterns of the characters.
After a lot of back and forth with their superiors they are permitted to go the Earth, disguised as humans based on the TV show.
Let's say they have a way of travelling that gets around any relativistic problems of time dliation ? The faster you travel, closer to the speed of light, time slows down for the persons traveling. That would mean that everybody else has aged horribly, and not the aliens. ? and they get to Earth instantly, in present day.
Because they have miscalculated about time it took the TV show to get to Earth, they stand out like sore thumbs when they wear 50s clothing, and talk with 50s slang, and all that jazz.
The TV show is in reruns so people recognize them, but since the actors have aged 60 years since then, people assume that they are young lookalikes who cosplay as the characters.
They eventually run into the actors.
Something like that maybe?