The entire idea of sinking a whole island comes with the obvious caveat that you would tell people which one it is, so they can emigrate if they so choose, thus bolstering the numbers on other islands and allowing players to bring with them their own personal history; the tales of a lost world, etc. I know it's more fun to be secretive and mysterious about these things, but at some point pragmatism has to play a role. If players can simply move their favorite characters, your entire dilemma is avoided.
And I think you're overplaying that dilemma, by the way: for the most part, players tend to spread over multiple islands. I have seen very few family pages where all the characters inhabit a single continent. I don't think people would quit as long as a thorough explanation is given as to why the island was sunk (just tack it right up there above the player's Family in big, yellow letters). That doesn't leave any room to interpret favoritism on the part of the devs, whereas now we are all left to deviously speculate behind your backs.
I can tell you now, if FEI had been sunk, I'd have quit. It wouldn't have been a "You sunk my favourite island so !@#$ you" ragequit, but it would have been a "I've put 99.5% of my BM time into FEI, and am not prepared to start over again from scratch" quit. Which in turn would have taken out my two character on other islands.
Given, I am the ruler of the largest federation on FEI so possibly have more time investment to lose than others, but I find it difficult to believe no one else at all would have felt the same way should their island have been sunk.
