I'm not from Miami, but I spent some time there last summer.
But what about the South side of the airport by The World Transport Press store, you know Airliners Magazine?
I forgot the name of the company, I want to say Just Plane Crazy, but they sell models and videos. It is on the southwest side of the airport. I don't know the names of the streets even though they are all numbers like 172nd st. and stuff and avenues run one direction etc. Anyway, next to that store is a furniture warehouse/store that has a parking lot with views right to the runway, the only thing that would obstruct the views was if there was a train parked there.