I used to fly 4-jets. Each time I had a new co-pilot in the sim, I used to brief that in the event of an engine failure he was to carry out the drills as quickly as possible, without saying anything, to make the situation safe. Without exception, I ended up with the situation where the wrong LP cock was shut, thus turning a single engine failure into a double. And the sim instructor timed the event from start to finish. Then we froze the sim and put it back to the start of the runway. The second t/o brief was for him to identify the failed engine positively, touch each control and say what he was about to do before doing it, and then do it. Again the process was timed.
The difference was measured in seconds; but the main point was that we were now flying on 3 instead of 2 engines. It does not pay to rush the checks. There is no circumstance that I know of where you MUST get the engine shutdown drills done in record time. Rather you should take that extra second or 2 to make sure you get it right...