I think the only way to settle it, if Russia ever does bring back the throne (constitutional obviously) is to usher in a new dynasty. The current Romanovs are so divided on the 'true ruler' that picking from any side would have backlash. Picking a ruler that is Russian, and primarily Russian sounds better to most people. Someone rightfully 'theirs' rather then someone who only possesses an nonfunctional title. Who's connection to their homeland died a long time ago and one they no longer share. The Romanovs can't really say 'no'; they have no power in Russia and their dynasty was founded the same way.
Of course it would probably be hard; if they don't pick someone in or connected to the government they would have to narrow their search. I don't expect them to start knocking on the doors like 'hello, want to be the Tsar of Russia?' but hey, have to start somewhere.