At least for a time, the deep state needed King. He was an acceptable alternative to the hard left radicals that wanted revolution, revenge, and plunder, and who were heavily funded by the Chinese Communists (i.e., Mao).
But what was Deep State’s involvement in having him executed? Perhaps, they were hoping to trigger an uprising, as an excuse to implement social controls (like they did anyway after 911).
I think they warned him repeatedly to rid his group of comrades and he chose to ignore.