Ken,
Meaning no disrespect, but we're talking about the British crown so while there may be "many forms...for Royal address" out there in the world. There aren't "many forms" in the UK. The situation for Arthur is no different than any other British monarch: one minute he was a royal highness, with the death of his parent, he became a majesty. Just like her present Majesty who went to sleep in a tree house as a Royal Highness and awoke a Queen. Additionally, he was never a "highness" always a "royal highness" and the forms of address are not optional and certainly not optional for the British peerage. Anyone who violated the norm would be courteously treated, privately dismissed as a lout, and never invited to return.
I'm not exactly sure what the Prince Regent has to do with it. He was "His Royal Highness The Prince Regent" until his father died whereupon he became one of the most unpopular majesties the British ever had. There should be a regent in the UK while His Majesty is gallivanting about. This can be a Council of Regency and need not be a member of the royal family, though this would be unlikely.
Respectfully, your humble and obedient uppity serf