Not withstanding some 'unusual' comments from '4468' your statements also give me pause KenV
Not sure what type you are flying but on a reasonably modern Boeing (757 and later)
while executing a coupled approach in low viz using a DH and not being able to see the runway at minimums I would most certainly fly the missed approach using the autopilot
one press of the TOGA switch will have the aircraft start climbing at 2000fpm and fly the entire MAP including entering the hold in LNAV in a very smooth, controlled maneuver.
That is the procedure at my Airline, why would you want to do this manually ? are you perhaps talking about a considerably older type ?
Of course if the automatics are not working correctly you disengage and fly manually,
as the EK crew should have done although the automatic functions appear to have been working as advertised in this case.