If I were unlucky enough to be single engine (or N-1 as we say now) I would divert to the nearest BIG airport. With a BIG emergency, given the choice, I'll choose the BIGGEST airport. I'll do battle (well, I'll let BALPA lawyers do that for me) with those who say I broken the rules after I have landed safely. And the way I see it, by landing as soon as possible, I am following the rules.