Hercs have been based in the South Atlantic for 26 years and have been tasked with Maritime Radar Reconnaissance and Search and Rescue. Amongst the many crews who have detached, there will be experience in davejb scenarios 1 and 2.
In 1993 there was a little publicised SAR incident involving a Russian merchant ship that sunk halfway (I believe) between Tristan de Chuna and FI. The rescue effort required multiple sorties at long range in difficult weather and pre-GPS. The effort required AAR, dropping of dinghies to pockets of survivors and 'conning' a nearby ship to the scene.
I am sure the Herc is not as capable as the Nimrod in some aspects. However the crews and aircraft are not the lame duck that other have alluded to.
For scenario 3, how about E3?