Was about to mention this. This was easily the most well-written story of the three given in the book (its premise is that JFK is assassinated in late 1960 by Richard Pavlick, an anti-Catholic, and that the ensuing constitutional crisis is resolved with vice president-elect LBJ rising to the White House).
It really focused on Lyndon Johnson's individual worldview and personality, how different they were from JFK's, and how it led him to interpret the Bay of Pigs, Castro, Khruschev, and the Missile Crisis differently. For example, whereas in OTL, Kennedy interpreted the Bay of Pigs disaster as a lesson in the importance of questioning the optimistic estimates of those in either the CIA or the Pentagon, LBJ interprets it as a sign that high-faluting bureaucrats like those in the CIA don't know what they're doing, and that nothing can beat the old-fashioned knowledge and experience of senior military leaders.
And Johnson's lack of internationalism and political career based on wheeling-and-dealing in the Senate cause him to interpret negotations with Cuba and the USSR through the same lens that got him through his domestic dealings with American Congressmen: that both parties in a negotiation were acting in rational, down-to-earth self-interest, which meant that a solution could be reached through just the right quid pro quo and compromise once people could agree on what they'd be willing to sacrifice. He doesn't understand that Castro and Khruschev were being motivated by different influences, such as ideology (believing fervently in a cause to the extent that they'd be willing to make great sacrifices to see their vision come true) and pride (not wanting to come across as weak and wilting in a confrontation with the U.S.).