B773 performance struggles at that those conditions.
Not so sure I agree with that statement. Perhaps a heavy 773 with a single engine failure would struggle in those conditions with it's climb out limit but both engines, at the end of the flight with minimal fuel? The climb performance would be more than adequate. The QRH puts the landing climb limit weight with F20 (landing F30, go around F20) for 49 degrees at about 300 tonnes giving approx 50 tonnes over MLW.
The difficulty is separating the 'training scenario' that we all get in the sim of majority single engine go arounds with the real life scenario where a go around will often be conducted with both donks operating.
Personally, excluding the possibility of severe windshear, I don't think aircraft performance will have been an issue but that is hypothesis on my part and therefore speculation.