Thanks for correcting my terminology; what I was getting at was that "Give her all she's got" should have been called for. Whether that's 'Full Power', 'Contingency', 'All ahead together' or whatever!
Then, as you also state, everything normal until safely away from the ground and at a safe speed until the Op Plt ordered the relevant engine to be shut down.
Even if the #2 was only developing 50% thrust, 3.5 engines' worth of thrust might have made the critical difference which 3.0 engines' worth of thrust didn't!