There is a breed of simulator instructor which takes the view that if you don't deal with scenarios exactly as they would deal with them, then you are incorrect. I think that this is a bit poor, but I've encountered it and had it described to me by colleagues many times.
What's incorrect is the attitude that there's only one way to skin a cat !
I can't resist giving my solution --- My personal preference would be to keep the engine going for as long as it did'nt cause difficulties eg cruise, descent, in fact, possibly all but the intermediate and final approach. It would require some familiarisation with the situation to determine the range of possibilities, hence my proposal is vague in terms of when to shutdown, or even if it would be necessary. My overall philosophy would be to keep te engine going for a long as sensible, but see below.
The Captain should decide who is to be the handling pilot. (the Capt. in my view should be handling in this case).
I would use any time available, or make time, fuel permitting (eg by holding) to :
(a) Try to resolve the jammed throttle problem.
(b) If (a) unsuccesful, very thoroughly review the potential shutdown procedure with my colleague, revising the need for confirmation by BOTH crew members of correct throttle/fuel lever/whatever etc BEFORE anyone moved anything to off/closed/shut. Some items of the procedure could be completed in anticipation eg ignition settings, de-icing system implications etc etc.
(c) Inform ATC and arrange a "calm" approach. Consider diversion to longer runway/better aids/better emergency cover/ better maintenance.
(d) Ensure that any shutdown would not be coincident with high workload phases of flight, especially the final approach. Basically decide to either shutdown or not to shutdown in very good time.
(e) Review the need and procedure for shutdown after successful landing. (won't stop too well with 77% N1 I'm guessing and reverse is locked out due to no idle throttle position).
(f) Try to decide how much degradation in landing distance might be incurred -- is the runway going to be long enough ?
(g) Review the procedure for relight of the affected engine, to avoid delay should relight be necessary, for whatever reason.
(h) Brief the cabin crew
(i) Inform the passengers, if considered necessary.
(j) Inform Company, time and workload permitting.
The above would need to be amended according to timescale and proiorities. I always remind myself throughout -- "Aviate, Navigate, Communicate" in that order of priority.
My main point, however, is that if X pilots contribute here, then there could easily be X proposed solutions to the situation and many of them would be just as valid as any of the others. No simulator instructor should dictate that their solution is the only one. To hear his suggested method, without obligation, would definitely be worthwhile, though. Maybe their solution would be better, in which case something gained !
Always willing to learn. Never seem to stop !
All of the above is just IMHO.