Well, with Goldwater being out of the running since his 64 fiasco, I'd say the only real candidate who could lead a right-wing takeover of the GOP would be his biggest fan, Reagan -- and I'd stipulate that for this to work, Reagan has to win the nomination and subsequent nomination outright, so the VP-ship isn't going to do it.
As to how -- well, there was his run in 68, but coming just two years after his election to the California Governorship, that was just something of a pipe dream. He decided not to challenge Romney for re-election in 72, which was smart, but did decide to try to snatch the nomination from Brooke in 76 -- and it doesn't look like that was ever going to happen either. Due to his age, his last chance would have been in 1980, but of course then Brooke was running for re-election -- as in 72, he couldn't really challenge an incumbent President.
So where does that leave us? Well, it looks like the only way to even open up a plausible Reagan win after Goldwater's defeat in 64 is to have either Romney somehow lose his re-election bid in 72 or have Udall beat Brooke in 76. And even assuming this happens, and Reagan manages to sell himself as the GOP's best shot at re-taking the White House, and he then beats McGovern in 76 or Udall in 80 -- even then it's not clear sailing for the right. Because -- and this is somewhat relevant -- Reagan was not "religious" in the way the CDP would understand it. Not only was Reagan a divorcee, he signed in CA the country's first No Fault Divorce law.
All told, it looks like after 1964, the Hard Right was just in too vulnerable a position to have any hopes of taking over the Republican party, at least before the Cold War was up -- and of course, once the threat of Communism was gone, American conservative philosophy -- even for the followers of Goldwater -- had to adapt...