I'm not sure how to word this, but I do feel its at least a fun topic. Basically, there seems to be the occasional ATL havoc scenario whether it be an atomic war, revolution, etc., or maybe just dumb luck in how events turn out that seems to give rise to all these otherwise out of left field presidents. As I recall, WoL,WoT seems to be position Goldwater last I checked in (whether that still holds or not, I don't know), and there's a TL on McCarthy as President. Reagan himself may be an example in real life; you have decades of Liberal dominance erode and then get over turned by someone who would be on the fringe only a few decades earlier
So my curiosity is to sort of make a check list of good out there/out of left field Presidents who would arise to the Presidency through conditions and circumstances.
Two come to mind for me:
Billy Graham
Graham was offered support to run for the Republican nomination for 1964. Albeit he was a Democrat by membership, if I recall he did consider it before his wife mad a ruckus over it and his better judgment made him decide to keep his religion and politics separate.
However, in Graham you have a very religious figure who commands many followers and is charismatic. He could also fall into that whole "Theological, Conservative USA" dystopia trope ala "Escape From LA".
So in a chaotic scenario where either something goes very bad post-JFK assassination or things are otherwise thrown into chaos or command a major backlash, I think it's an interesting possibility. It need not even be 1964.
Barry Goldwater
This one may be pretty obvious. He's a Conservative in an era where the New Deal Coalition dominates, who opposes big government and the welfare state when its in no way fashionable to do so. He supported Civil Rights, but was not supportive of the Civil Rights act of 1964 and was hence viewed as a racist by opponents, supported the creation of tactical nuclear devices with small enough yield to be used as a common weapon, and believed in all sorts of other things that were in no way popular during a Liberal era. He was also less than thrilled to run for the White House from what I remember and was more or less pushed to run by hopeful GOP Conservatives.
Goldwater could win in a few ways. Firstly, the Johnson scandals could be brought to light (Goldwater disliked Johnson because Johnson was a dirty politician, at least in Goldwater's opinion) leading to a far closer election and perhaps even victory. Or there is the run of the mill chaos event, whatever it may be (atomic war, President Micky Mouse, etc.)