As soon as JFK died I would've tried to convince Goldwater not to run, allowing Rocky to win the nomination and take the inevitable fall, which would put Goldwater in a good place to run in 1968. If I coudln't do that, I'd convince Goldwater to choose a moderate, prominent Rockefeller Republican like Margaret Chase Smith, to avoid scaring as many moderate Republicans as Goldwater did in real life (Goldy mainly chose Arthur Miller because he drove LBJ nuts). I also woudl get Goldwater to ruthlessly attack LBJ for using smear tactics such as the Daisy ad and allegations that Goldwater was racist (which would involve Goldwater trying to rationalize his vote against the Civil Rights Act of 1964 so that he doesn't look like an actual racist). With this beign said though, it'd still be a losing fight, but I could see Goldy doing a little better.
That's William Miller, not Arthur.