I'm a life-long New Orleans resident, college counselor, teacher, and writer. I have travelled many countries, but my first love is this city--for its whimsy, blasts of light, and many weathers. You should come here too.
The streetcar is the slowest way to get to the French Quarter, for sure. I recommend the Magazine Street or Annunciation Street bus lines. Stops for both are two blocks away from the apartment, and their schedules are punctual and reliable. Certainly would have pointed you that way had I known you were experiencing hassles. Very sorry not to have known.