As I understand it, King Olaf V of Norway was born HH Prince Alexander of Denmark, and got elevated to the rank of Royal Highness only after becoming the new crown prince of Norway. Unlike the Greek royals, who remained in the Danish succession, the Norwegians were made to renounce their titles and rights to the throne of Denmark. As for the Greek royals: as prince of Denmark, they would have been only Highnesses, but for the fact that they were member of the royal family of Greece they were Royal Highnesses. Is all this correct?

Forward flash to 1917: I believe that Queen Frederica of the Hellenes was born a princess not only of Hanover but also, Great Britain. In the United Kingdom, however, she would have been only a Highness, as a remote male-line descendant of King George III (he was her patrilineal great-great-great-grandfather). As it was, she was a Royal Highness at birth only because of dynastic membership in the Hanoverian dynasty -- notwithstanding the fact that the house was deposed in 1866. So the forfeiture of her British
title (several months later, when King George V of Great Britain issued Letters Patent specifying eligibility for titles and styles) became irrelevant. Is this correct?

If so, these cases point to odd situations of persons belonging to two houses, where the qualifying rank was different. But if I understand correctly, the higher qualifying rank always applies. It would certainly be awkward to call somebody "His Royal Highness Prince X of Greece, His Highness Prince X of Denmark."