Hi, Clive
I don't know that use of "we" necessarily means the king and the country were taken as the same entity. The OED, a mere dictionary for a British dialect of your language, quotes "We, Dermot, prince of Leynester (1425)" as the oldest use of "we" of that usage. The OED says the "we" was commonly followed by a personal title or name. Anyway, even if what you told is true, I am wondering if it could be an evidence to support the opinion "England's King" is a natural expression. The OED is saying in its entry of "of" about the issue on England's King and the King of England as follows:
"OF" XIV. In the sense belonging or pertaining to; expressing possession and its converse: "the owner of the house", "the house of the owner".
Formerly expressed by the genitive, and still to some extent by the possessive case (with transposition of order). The use of of began in Old English with senses 47, 48, expressing origin. After the Norman Conquest the example of the French "de", which had taken the place of the L. genitive, caused the gradual extension of "of" to all uses in which Old English had the genitive; the purely possessive sense was the last to be so affected, and it is that in which the genitive or "possessive" case is still chiefly used. Thus, we say the King's English, in preference to the English of the King; but the King of England in preference to England's King, which is not natural or ordinary prose English.
You are speaking the American Language which is spoken in a country where Martin Luther King was born, and so I don't say "England's King" is completely wrong as far as you concerned.
Best wishes,
paco