I think the map which bobloblaw constructed. The idea that JFK going to Dallas to bolster his support in Texas in '64, suggests to me that LBJ was staying on the ticket and the fact that Texas was very much on JFK's radar, meant that LBJ was central to JFK's reelection prospects. Symington he didn't much know about, while LBJ whatever the personal issues were, was easier to keep than dump. Symington wasn't owed anything by JFK, where as LBJ ensured victory for JFK in 1960. There was also the matter of institutional and political memory to consider. Keeping LBJ was also tidier politically and JFK was no fool.
You do understand JFK would have later met with Coke Stevenson?
I suspect Stevenson wanted Kennedy to convince Connally to lead a coup against Johnson. Kennedy's reported planned meeting afterwards with Stevenson is actually one of the few pieces of evidence favoring a Johnson-assassination plot against Kennedy.