Regarding A/T on/off: I digress slightly as this comment is not specifically about W.S. escape. And firstly I have to disagree with Boeing's 1 size fits all philosophy.
On the B737 classic the TCAS RA manoeuvre was disengage A/P and follow the red prism guidance. You left A/T engaged, which I thought a splendid idea. In the stress of the moment speed control was one less thing to relax about; the escape and the recovery afterwards.
On the NG Boeing disconnects A/T. When I asked Boeing pilot he said it was to comply with Boeing's philosophy of manual flight = manual thrust. How pedantic is that? I suggested they had introduced a massive threat, and perhaps after the first RA followed by stick shaker they would be reviewing their procedure. There was little reaction, but a note was made. On your day, when you are at the sharp end wrestling with the bronco you may choose to use the depth of airmanship you have and do what is necessary rather than dither around.