I think they ought to discard the ill-conceived "succession law" of 1797 [only enacted because Pavel hated his mother.
Instead of going through all of this convoluted rigamareau, trying to extend the succession into distant branches of the imperial family, they ought to do what most other monarchies do- simply have the closest relatives to the last tsar take their place as the current imperial family.
Alexander III, Nicholas' father, is not without descendants, as we all know. As Nicholas is dead without descendants, and Michael is dead without descendants, they should simply pass the throne to the descendants of Xenia Alexandrovna, the next oldest child in the family. The oldest son of the oldest son of Xenia should be Tsar.
If Xenia were to run out of descendants [which I don't think will ever happen] then the throne should go to the Kulikovskys.
If the Kulikovskys run entirely out of descendants, and there are thus no more of the line of Alexander III, then and only then, should the descendants of Grand Duke Vladimir make a claim to the throne.
After the descendants of Grand Duke Vladimir would die out, then the descendants of Grand Duke Paul might inherit the throne, first the Ilynskys, and then if there were no more Ilysnskys, the descendants of Prince Lennart of Sweden.
By the way, did Prince Lennart of Sweden have any sons?
All of this confusion [with second and third and fourth cousins claiming thrones] only makes the idea of "restoration of the monarchy" more difficult. In England those second and third and fourth cousins would be peacefully playing cricket on their estates, very well aware of the remoteness of the chance that they would ever inherit the throne.
Point being: Let a descendant of Alexander III rule.