Interesting case this one. I remember about 10-12 years ago QF had a -400 coming LHR-SIN and they shut down an engine over Iran due to an oil pressure problem. QF SOPS for the -400 stated that the aeroplane must go to the nearest Suitable Airport, the definition of suitable being a company Main or Alternate with appropriate weather/ fuel reserves.
I don't know what the weather was like at en-route ports like Karachi/Mumbai etc but the decision was made that the nearest Suitable was Singapore and they continued and landed safely.
It is a long time ago and as I said, I don't know what the enroute ports were like, but it seemed a interesting decision at the time. I also wasn't privy to the company reaction either.
This BA case has been covered extensively in Rumours and News. If operating under QF SOPS, I doubt you could justify going past JFK. Seven hours over the Altlantic on three engines when a Company Main airport is sliding below would not be what I'd personally feel comfortable with.