The following quotes have really got me wondering about the way Malcolm X influenced MLK's reception nation-wide.
Malcolm X on Dr. King: "I'll say nothing against him. At one time the whites in the United States called him a racialist, and extremist, and a Communist. Then the Black Muslims came along and the whites thanked the Lord for Martin Luther King."
Dr. King on Malcolm X: "You know, right before he was killed he came down to Selma and said some pretty passionate things against me, and that surprised me because after all it was my territory there. But afterwards he took my wife aside, and said he thought he could help me more by attacking me than praising me. He thought it would make it easier for me in the long run."
My searches here thusfar give me the impression that /u/koglerjs might be able to provide some insight on the subject; I'd love to hear your thoughts!
I'm not entirely sure what clarification you're looking for. You seem to know how each individually reacted to the public image of the other through the quotes you've posted.
Are you asking how people perceived the contrast in their public images?
Well, I think coverage on MLK is fairly well documented. But I have a feeling that it might be useful to link you to some of the mainstream documentation of Malcolm X and the Black Muslims.
First is the Playboy interview of Malcolm X--the old joke that you read Playboy for the articles once had a tinge of truth to it. This is a demonstration of how Malcolm X intended/created his public image.
Second is The Hate That Hate Produced, a video documentary of Elijah Muhammad's movement. (Pay attention to the section titled 'Modern Analysis.')
The only other thing I can think of is to find quotes from MLK on the subject of Malcolm X, but you've done that. Really, I'm not really doing much more than pointing you do more sources on Malcolm X's public image, so feel free to ask additional questions.