...would it not be a natural reflex to retard the thrust levers to idle in an attempt to try a last ditch effort to spool up the engines manually, an attempt to initiate a thrust increase from idle conditions?
Not for anyone who was a jet pilot.
About the only time you'd think of retarding a thrust lever when you're undershooting, in an attempt to 'cure' an engine problem, would be if it was surging badly - and this is not the case with BA38.
When people talk about manual thrust on the 777, they mean without the autothrottle engaged. All the A/T does is try to move the thrust levers to satisfy demands from from the A/T computer; when you take it out it means you have to move them yourself. The thrust levers have sensors on them which provide position data to the EECs; that's it. The engines are FADEC = Full Authority Digital Engine Control: there is NO 'manual' control; the only thing you can influence is the mode they operate in - the RR Trent has a 'hard alternate' mode you can select from the flight deck that references N1 instead of EPR and removes some of the thrust (overboost) protection.
It seems obvious to me that the flap retraction to 25 was only to clear the fence and maybe make the runway. Nobody in that situation with two sick engines would attempt a go around. No pilot on the face of the earth would have attempted a go around. Why even bring this up? If they had enough power to go around they would have just landed.
Says it all, really.