Which British king wrote out his declaration to abdicate several times, writing that he was no longer of "utility" to his people, but did not finally abdicate?

I don't know, but I will guess George III.

George III tried to abdicate, in favour of his son, after Yorktown. So he paved the way for another "George the Third" to make an inadequately assessed and carried out adventure where he misunderstood diplomacy and the feelings and sensitivities of the local people. At least the later George hadn't France and her fleet to worry about...only Syria and Iran .