I can speak only for the falcons,
the falcons meet stage 3 or 4 limits ONLY when reducing N1 ( around 10 to 14 percent). A noise abatment is not a race to altitude, it is a way to reduce the noise, would it be close or distant. In any case it calls for a thrust reduction.
If you take the 7X out of LCY, the N1 reduction is quite impressive and it is done at 400ft....
ICAO is asking for a thrust reduction at 800ft, shouldn't it ring a bell ?
Nethertheless, our engines are making noise on take Off, and to reduce it, you need to reduce thrust. REad carefully, Jepp Book1 ATC pages 251 and on.
Jar Ops is even clearer asking for every operator to have noise abatment procedure and to use it every time for every airport.
The tendancy through airports is to design specifics procedures for their departures. The only advice is to read the pages 10-4.....