Your reception location is Between a Rock and a Hard Place.
All methods and ways of reception are , Nixed.
My best recommendation for reception at your location , that will also be , Nixed , is.
Put a long mast / masts pipes / in a bucket of concrete out on the balcony.
The Long mast /mast pipes - Must Be - Long enough to extended a Winegard , FV-HD30 antenna , above the roof.
Aim the FV-HD30 the direction of South. Here is how to aim antennas ,
http://www.kyes.com/antenna/pointing/pointing.html.
Here are places to buy antennas and etc. .
http://www.winegardirect.com.
http://www.solidsignal.com.
http://www.amazon.com.
The balcony door will be open enough for the coax to go into the apartment and the door is sealed with duct tape.
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The other option is to move to a apartment , etc. .
That has a good / windows / balcony / patio / exposure to the , south east , south , south west.