I have a feeling that Goldwater wouldn't run for the Presidency again, given '68 would be the one chance he would have of getting into the Senate again (having already decided against running in '64 to seek the nomination), or he would have to wait, at the very least, until '74.
I absolutely agree with this assessment. Assuming he loses the nomination at or after the California primary, Goldwater will have just given up his beloved senate seat in pursuit of a nomination that he did not want for an office he did not believe he could win. I imagine that he will, in his very dyspeptic way, tell off the William Buckley and co. and plan on making his 1968 comeback.
If in 1964 Wallace pulls away some of those deep-south states that went for Goldwater, I think he'll be emboldened to challenge Johnson more directly in 1968 by running against him in the primaries. Looking at the primary schedule I see three possible wins in Wisconsin, Indiana, and Florida. (The first two states are ones in which he performed quite well against Johnson surrogates in 1964, the latter is a neighbor to Alabama which leads me to believe he'd have a regional boost.) He'd have enough support in the rest of the states to skew the results (particularly in California and Pennsylvania). The result could be a convention in which Bobby Kennedy, Eugene McCarthy, Hubert Humphrey, AND George Wallace are all competing for the nomination. Wallace probably wouldn't win and would know that his chances were slim, so I bet he'd be trying to play king-maker. And if you thought things were bad in Chicago IOTL, just wait until Wallace or his supporters get on stage.
I could imagine that Reagan would still give speeches for whoever the nominee was ITTL unless it was Rockefeller. I doubt he would have a problem speaking on behalf of Scranton or Romney, though, and he may still gain notoriety for bridging the gap between the moderates and the conservatives if he's willing to work with the other side. I imagine it would be enough to get him the California governorship in 1966.
I'd be looking, however, at Nixon as the parallel to 2008 Hillary Clinton: the candidate who seems to have the nomination sewed up but for the efforts of a dedicated anti-establishment force. The candidate wouldn't matter much to them so long as he's sufficiently conservative. I imagine as in 1968 the conservative wing is going to have created a similar campaign machine to 1964 and, like in 1964, will start campaigning on behalf of a candidate without really getting him on board first. My bet, as I've mentioned a few times on this board, would be Senator Pete Dominick of Colorado who had the conservative credentials and was infinitely more electable than Goldwater; if not him then maybe Governor Jim Rhodes of Ohio who hasn't been tainted by Kent State or allegations of corruption yet. I think it could legitimately be a close nomination if the conservative forces hold onto, and redouble, their positions of strength between 1964 and 1968. Nixon may be denied the nomination at the convention, having failed to cow the conservatives.