I think the issue here is why the pilot deviated from the rational to the irrational...
I think one possible reason, something that has been touched on previously, is that he wrongly assumed his aircrafts situation was worse than it actually was.
In the heat of the moment, of a multiple heavy bird strike, he wrongly assumed that he had had a "Sully" moment. Both engines losing thrust and unlikely to get back...
His reaction appears to be one of panick. His first thought was to get back to the airport and any procedures and rational decision making went out of the window at that point.
If he had lost both engines he would not have been able to make a turn and return to the airport. His only option probably would be to attempt a crash landing on open land or water immediately ahead.
If it had been the worst case senario he probably would have had limited options... But he still made the wrong decisions; under a moment of intense pressure he lost the plot and having set out on the wrong path continued on it.
I think that the most helpfull things to be stored in the back of his mind would have been a rehearsal of a worst case scenario on take off. This is the thought process of thinking that if you cannot save the aircraft maybe you can save people on the ground or with a lot of luck make a successful crash landing. If his mind had rehearsed the worst case then maybe, and it is just a maybe , he would have been able to make more rational choices and react to facts rather than imagined circumstances.
I think that the assumption that he was a bad pilot or did not know what the correct procedure was, in all likelyhood, not the case. It appears that he made the very human error of failing, under extreme stess, to behave rationally.
Luckily for all, the outcome was a good one. We all, at some point, will likely face a s#$t has hit the fan moment...we all hope that we will deal with that moment gracefully and rationally. To think that we are above failure is foolish. Of course, in the circumstances I doubt we will ever know the pilots perspective, but I doubt that he will happy with his performance.
Simulation only goes part of the way to prepare for high stress events...