Rightful heirs? On base of what? The only legal document, or document which had legality, about the succession to the throne of Romania is the Constitution of the Kingdom of Romania. That state was seized by the Communists and the royal family was exiled.
Until 2007 the succession was based on that Constitution. The same Constitution which grounded King Michael's kingship, the same Constitution he once solemnly pledged to defend and to maintain.
That is the only document which ever had legal validity. The "Fundamental Rules" set by King Michael (and not so very fundamental since his enthusiast scrapping) is a private document. It has zero comma zero legality.
When someone starts a lawsuit on base of these Fundamental Rules, then the Judge will say: "Excuse me: Romania is a republic. There is no King. There is no throne. Your document is a particulier correspondence. There is no any jurisdiction for this Court or the State on base of that document".
With other words: the succession has ended with the death of the former King. Anyone is as free to claim the throne. The closest are the Hohenzollerns, based on the only document which ever had legality but they -wisely- remain far away in Baden-Württemberg. For the rest any claim is as thin as one night's ice because based on private conviction and pretense.