At climb out you get N1, N2 and EGT showing well above red line.
When you level of to deal with the problem the airplane is accelerating even with the autothrottle off, the bad engine at idel and your good engine at idel too.
What check list is the most appropriate?
Is this a "what if" or did it actually happen in a simulator?
I just don't see how the most screwed up engine in the world could exhibit all those symptoms at the same time. Something about the engine cycle seems to limit this even without a sane ECU, FADEC etc.
From a cause-effect point of view, of course you always fly the plane first and take your time about sorting out what engine is causing it. Eventually you will see that an engine is too high and you will shut it down either by its control unit or the pylon.
There is nothing bad that is going to happen to the airplane while you sort the engine out, in spite of redline this and redline that,.