Your choice of options, with no latitude, is a poison chalice
We are frequently asked to drink from that cup unfortunately
Ok, people seem to be fixating on the 100 miles, let's say it is only 50 miles or less. The basic question is, and again assuming an OEI deck landing is not an option, is it better to:
Continue the approach and land on the deck and fight the fire (if there really is one), or overshoot into IMC, complete the drill and proceed to the land based alt, overshoot and attempt to remain VMC, run the fire drill and if things go bad (can not put the fire out etc.) ditch beside the rig?
This is only a thinking exercise and looking to see what trainees thought processes are.
No drills, land on the water, get the rafts out. Could get expensive if you set the rig on fire as well - that's if they don't push you off anyway.
The above is an option "C" to consider.
Oh, and did I mention it was night
