Thank you again, Uncle Fred, for the instructive comments and the courtesy they came with.
On reflection, I think that I have probably been throwing dust in my own eyes by raising the hypothetical "worst case". I think that I displayed enough ignorance to mislead myself and to demonstrate that I have confused myself and misunderstood what little I do know.
The short point is that there are now so many two-engined aircraft flying under ETOPS rules (and the number is increasing), and they have been doing so for so many years, that the incident is scarcely merits the adjective "hypothetical" -- it would already have happened, and it would be common knowledge in your profession. Over time, the longer it hasn't happened has made it less likely that it might; what was planned to be unlikely eventually became wholly improbable, and is now for all practical purposes impossible.
Moreover, there is an absurdity: planning a diversion for a planned diversion leads logically to a regression ad infinitum which can be avoided only by deciding to stay on the ground: "Ladies and gentlemen, this is your captain speaking. We have decided any flight such as the one we originally proposed to undertake is too dangerous. This aircraft is in perfect condition but will be dismantled and sent as deck cargo to Atlanta, and at your choice you will be issued with tickets either for the same voyage or for an exciting overland safari....."
Seriously, however, does anyone watching this topic know of a case where a flight was delayed, or re-routed before entering the ETOPS area, because a planned diversion had become unavailable? The mind boggles at how one would explain this over the PA!