Sorry but I do not necessaryly agree with the idea that a Mayday is not necessary asap.
It is vital that WHEN TIME ALLOWS, to warn ATC that you are in trouble.
Why?
1) they will not interfere when seing you swerve rom flightpath
2) they can reroute, hold all other traffic asap freeing your way to whatever course you must go
3) in case of you being behind the aircraft and headingmtowards terrain, they can warn and offer escape vector. ( in a radar environment)
This is of course when in a terminal area below msa etc...
Obviously,maircraft under control comes first, then memory items, but you are with two on the flightdeck.