I favour a hereditary line originating with George Washington. Tho I believe his stepson via Martha predeceased him. Frankly, I would just get a nephew since there are other surviving members of the same 'blood'. So far I'm not advocating any 'butterflies' but just generally discussing it.
With the formation of the Empire of Brazil Pedro I was granted some not quite deliniated constitutional powers that were to permit him to influence government. I would expect that any power granted the Crown, like recalling the Congress from recess or holding them over until they work things out, will be clearly spelled out in the Constitution.
Regarding titles, undoubtedly there would be a US College of Heraldry. I think it would follow the English House of Lords, tho probably with Grand Dukes as titles for members of the Royal Family. Franklin would Duke of Philadelphia, perhaps Robert E. Lee would be Duke of Arlington (which I think Turtledove does use in his fantasy ACW books).
About 'Guardian of the Constitution'. I really see that as part of the King's full title along with 'Defender of the Faiths' or 'Defender of the Faiths and Freedoms'. Perhaps we have:
George, By the Grace of God, King of the United Kingdom of America, Guardian of the Constitution, Defender of the Faiths.
which becomes:
George III, By the Grace of God, King of the United States and of the Confederate States, King of Texas and California, Emperor of Mexico, Guardian of the Constitutions, Defender of the Faiths.
Something is missing and I'll think about it later. Something to do with 'possessions overseas' etc.
My earliest ATL, even before the advent of the WWW, was on this particular subject. I've got reams of paper typed out on this subject. However, I actually see the title of King becoming superceded by that of Emperor. Just because the King meets and befriends Emperor Norton.