“The Operator in question here does not allow the use of manual thrust, or raw data, at all.”
in this case neither pilot realized that the wheels had touched down and Auto Go Round had been inhibited, there must be cases where GA has to be done after touch down, therefore manual thrust would have to be used.
Is inhibiting auto throttle as soon as the gear touches down a good idea and why is it not cancelled when the GA button is pressed
That aside, because following through every automatic action monitoring becomes casual, in a Go Around situation which is uncommon I would be on those throttles immediately as would any GA pilot, rules or no rules.