MMMMMMMMMMMm........
.......What about confirming you have a genuine problem before taking precipitate action. I believe it is still the case that you are more likely to have a false indication of engine fire rather than a genuine one.
I have said before that if you get out alive and brought everyone else on board with you then you made the right decision.
I love these challenging sim scenarios but I wouldn't rush to judgement on the outcome. There are some heart-rending stories from real-life accidents where the crew made all the right calls ........ except the last one....... and it killed them. If you read all the accident reports you can get your hands on you will come to realise just how much influence 'lady-luck' has on the outcome.
Personally I would go for an AEO rig landing unless I had some other indications (smoke,smell) that all was not well. At that range the deck crew should have you in sight and may be able to tell you if they can see any signs of a problem. If I had a genuine fire then I would try to put it out whilst the CoP flew towards the rig. An OEI landing in the water if the fire doesn't go out - burning helicopters not very welcome offshore! That said if the conditions for ditching were extremely unfavorable then bugger the rig's problems I would do an OEI landing on the deck. (If conditions for ditching were that bad there is probably a strong wind and I don't think OEI landing would be all that problematic although wind direction may be a factor).
Years ago we operated the Bo105 offshore and the nearest alternate was 187 miles away. We had to carry alternate fuel for all our infield shuttles but I don't think any of us contemplated a 187 mile flight on one donkey on a winter's night. It was going to be an OEI landing come what may. Fortunately the Fulmar had a chinook-size deck.
G