BOAC Astraeus,
Boeing do not specifically mention it, but it is common practice to disconnect the A/T when performing such a manoeuvre.
Reasonable comment, but given the Recovery Manoever doesn't specifically require it, and in this instance it adversely affected the recovery (because of A/T issue) it leaves a widening gap between training practices, procedures and the (degraded) hardware.
Or does this caveat come in to play....................from QRH
--------------------------------------------------------------------------------
While every attempt is made to provide needed non–normal checklists, it is not
possible to develop checklists for all conceivable situations, especially those
involving multiple failures. In some unrelated multiple failure situations, the flight
crew may combine elements of more than one checklist or exercise judgment to
determine the safest course of action. The captain must assess the situation and use
good judgment to determine the safest course of action.
In some cases, the crew may need to move between two checklists
---------------------------------------------------------------------------------
Laurel and Hardy were flying that approach
You need to retract that one Rainboe, or risk losing a great deal of credibility