Let's not forget the PF did two things perfectly after the loss of the autoflight.
"I have the controls". Perfect.
Lyman: One thing....
I have the controls". Perfect.
Nothing from then on was perfect. Whatever he did to counter the right bank/nose down was certainly NOT executed anywhere near perfectly, with the end result being the same outcome as you postulate would have happened had he done nothing... just a number of seconds and wild ride later.
I have steered clear of commenting for a very long time, primarily because we have received nothing new to comment on. But you woke me up.
Back to silent mode.