Not a real bad stream-of-conciousness interpretation of history, but you really need to re-think this line “So they spent most of his term trying to undermine him (LBJ), to the point where he refused to run for reelection.”
Reality:
LBJ was so unpopular because of his war, he knew he could not win his own primary - exactly as Truman was primaried out 16 years before because of his own war in Korea.
They very actively tried to undermine LBJ. The Kennedy faction demanded from him that he keep JFKs entire cabinet, and thus agenda.
“The Great Society” were not LBJs ideas, though he was tasked with “arm twisting” them through congress, mostly against his fellow southerners, who remained in congress despite being stripped of power in the party apparatus.
Most of the war effort was handled by “Robert McNamara’s band”, who worked with direct management of the war by congressmen and senators. McNamara’s philosophy was that the war could be run like a business.
As you look at the timetable of the changeover from the old school to radical leadership, you can see almost to the day when the radicals turned, as a group, against the war. Generally solely for political reasons. Oddly enough, though Humphrey was too left wing for the southerners, he was far too right wing for the radicals, who only found their candidate in 1972 with George McGovern.
So though the southerners split right, first, the radicals were itching to drag the party left.
It all goes to who went against the war, and when.