Oh dear, I was really hoping this would turn out to be something like a propellor issue, as that would give a reason for the performance shortfall that did not involve mishandling.
The upshot is that when you have an engine issue (and it does not matter what it is), that dud engine is not important. The important issue is to ensure the aircraft is under control, and on a safe flight path. That may include using extra power on the good engine, but even minor things like identifying the failed engine are unimportant at that early stage. Rudder will be needed, in very large doses, and you DO NOT look to see which engine has failed to work that out. Rudder is applied as needed, by feel.
When the procedures are being carried out, one pilot should be flying the aircraft, and the other carrying out the checklist items. The flying pilot should only become involved if the procedure calls for an action that can't (readily) be reversed. So, a fuel control switch should be confirmed by both. There is still no hurry. The engine is already dead, leaving it turning for a little longer will only make it a bit more dead.
Flying the aircraft is by far the most important activity. Even if no checklist items were carried out, if the aircraft were just flown, most things would allow quite a lot of time before you really need to resolve them. In the RAAF I recall being told that the first item of all checklists should be to reset the clock...it gives you something to do, and does no harm...move on once the brain has properly processed what is happening.
In this instance, once both engines are shut down, it is exceeding unlikely to get a relight, and power, in the time remaining. Pointing the aircraft at a safe(ish) spot on the ground and keeping it under control whilst you glide towards it, would almost certainly have given a better outcome.
(oops ATR's)