Climbing into cloud won't kill you. Flying around at 300 feet over water at night in poor vis with both pilots concentrating on fires drills just might.
Epiphany, where does it say "at night" in the first post?
When performing emergency drills at least one pilot should be flying the aircraft - basic CRM.
Having spent hundreds of hours flying low level over the sea I admit that emergency procedures are challenging under these condtions, but that is also the case when IMC.
It will take 40-60 sec to approach the rig, how much longer would you like to fly with an engine fire that does not extinguish?