As I think King's letter describes, inviting excessive force was not all that was needed. Neither Birmingham police nor Albany police were publicly violent. Winning the Civil Rights battle required shaming the Southern White Majority from a position of silence and complicity with firmly the entrenched racist power structure. His Letter from a Birmingham Jail implored "Christians" to act like Christians.
I am curious as to which "philosophical heirs" of King you believe want to "make [America] Africa".
You nailed it. This is why he was ultimately effective. America sees itself as good, it aspires to be good; he called on it to live up to its own ideals. That, and the shock of his death, was the nail in the coffin of the Jim Crow system.
Things are not perfect, and in a human world will never be. But the kind of racial repression that existed prior to King, died in 1968 with his death.
It is common to read of his flaws of character, as his critics try to remind us of his ordinariness. Every reminder of his ordinariness makes me admire him all the more. There are millions of ordinary people in the world, all of them flawed in some way. Out of those millions only a very few stood up. Out of those millions only a few will ever make the kind of difference he did.
Those I saw on the morning shows today celebrating King day with completely African music. Seems dumb to me. King wasn't calling for the "African-ization" of American blacks---he was calling for American blacks to receive their full rights under the Constitution.