Lonewolf 50 Themental and congnitive process, when you are doing this on instruments (which I presume AF 447 crew were, as it was night and the Wx was bad) is to set an attitude in balanced flight and trim to hold that attitude in all three axes. (Plural of axis)
What I was taught and used to teach was to trim nose and rudder first, aileron last, to avoid cross trimming, but such technique is probably model dependent.
i understand that this is a target way to continue the flight, trim to hold altitude and speed as before
but with high altitude und UAS is it not much saver due to more aerodynamic stability to set trim for an auto-stable slow descent (flightpath mayby -3 deg?) with not so much trust, lower risk of unexpected climb, searching a lower FL with a major speed range, thinking about the CG ..... is it not much more essential to recover stability than constant altitude