1. If the engine is still running, there is no severe damage yet, right?
2. To PREVENT sev.dmg. use the limit/surge/stall chlst.:
Condition: One or more of these occur:
•Engine indications are unusual (yes)
•Engine indications are rapidly approaching
or exceeding limits (yup)
•Unusual engine noises are heard (dunno - were there?)
•There is no response to thrust lever
movement. (yes)
Objective: To attempt to recover normal engine
operation or shut down the engine if
recovery is not possible.
On the other hand: I really do not see the problem here. The objective is to shut down the engine - why would it matter which checklist you use? Pointless discussion!
How about just telling the F/O and instructor: I am the Captain, and I decided that we had to shut down the engine. The best, and most efficient way to this was to perform the memory items for this. Even though the shutdown is not included as memory items in this particular checklist, I did it anyway because it is good airmanship and excellent judgement/captaincy etc. etc. etc.
Problem solved. Case closed.