Seems to me that the Romanovs going into exile would be the most expedient compromise solution--but it's hard to imagine any of the neutral northern monarchies (Netherlands; Sweden; Denmark; Norway) allowing them in. My guess is that they'd wind up in Spain pretty much from the outset, where they'd still be today albeit in relative obscurity after nearly a century.
AFTERTHOUGHT: if, by any chance, one of Nicholas' great-great-granddaughters happened to be a real babe, perhaps she might attract the attention of either Prince Harry or William in this day and age. Come to think of it, aren't there some offspring of the Spanish royal family that are rather attractive?