Where are the METAR's when you need them 
found the 29.79 QNH on the audio recording
My crude estimate, it's more around 700-800AGL range, concur with previous poster around 1000ftAGL, when passing abeam the tower, but already with a decent RoC.
And a Topgun style (the movie) lateral separation.
Whoever kicked the crew back into reality, did a great job!
But it's another tower I would be more worried about (although this one, most likely, had no people residing in it).
They were really aiming for 'The Korean Church of Queens' with its 60ish feet tower+cross, with a positive RoC only just about to kick in.
And laterally, within a wingspan or so... even too close for Maverick
