I'm not defending the crew here, nor do I fly airliners or fly professionally, and have not read the whole report or all the replies. Just wanted to play devils advocate a little
:
Two ways to lower your VMC (or whatever they call it in the airline world) at full gross weight if you don't need to climb is: get the gear out (adds keeling and stability) and/or reduce thrust on good engine.
1. Maybe it's possible that the captain had another partial bird strike/or somehow other performance issue where it was
safer to not add full thrust on the working engine. Or maybe the
thought he did and wanted to assess.
2. Maybe he was close to entering a dangerous VMC induced spin situation and reducing the thrust was his only way to get out of it when he ran out of altitude.
3. Maybe he reduced power during final manoeuvring to position himself correctly and allow himself to bank steeper without worrying about assymetrical lift etc, especially if procedures/terrain/traffic didn't allow him to do it into the good engine.
4. Maybe he opted to prepare for an emergency landing in the flattest country on earth and extended gear for that.
5. Maybe the extended gear to add stability?
It doesn't explain all of it, but could be a possibility. I've myself had a partial engine failure in a twin and know how confusing things can get. And the one thing that will instantly solve all your problems in assymetrical flight - except the obstacle clearance one (which wasn't a factor here) - is to reduce the power on the remaining engine. That's the fix-all.