However, in the time it takes to get to 3,000’, one would have hoped for an opportunity to sort things out in terms of pitch trim and automation. Even if you just let go and engaged the autopilot, it would sort itself out to some degree
I see what you are saying but I don't think it is practical in this particular circumstance.
I departed two weeks ago at a weight close to what they would have been ( mid fifties) and even with a reduced climb thrust I was holding significant forward pressure on the yoke as we cleaned up and held nose down trim for two or three seconds continuously. That is normal, but I would not have liked to let go of the yoke in order to engage the a/p prior to adding an appropriate amount of trim. This situation would have been much worse because of the thrust applied. What I am saying I guess is that I don't think automation should be used to get out of a situation. It's a great tool to use and may prevent you getting into the situation, but once you are there ( 100%N1 18 degrees NU in this case) then stabbing at buttons is not the answer.
I think this comes down to the PF's brain operating in a degraded mode due to fatigue, which lead to inappropriate actions which then could not be recovered from.
The antidote to illusions is fast reliable mental processing of the visual information presented on the PFD, with good training this counters the 'seat of the pants' illusion. If you are processing information slowly or not at all, the illusion is all you have to act on. So if they do run with an 'illusion' it still suggests fatigue in my mind.