Not sure Hatfield would be picked by Reagan for a running mate (Hatfield was probably one of the more liberal Republicans in the last 50 years; and even the fact he and Richard Nixon shared a mutual friend in Billy Graham wasn't enough to ensure he'd get the #2 slot in real life).
Maybe Ronald Reagan would have picked Richard Nixon as his running-mate in 1968, although Nixon might not be eligible to serve as Vice-President for another term. If not, either Gerald Ford, John Tower or Winthrop Rockefeller would have made decent choices as well.
Think I've seen an similar expression made elsewhere; but there's no question by 1968 Nixon wanted to be "the man". Can't picture him settling for the VP slot again (if he could at all).
As for the others: John Tower wouldn't be much more experienced nationally than Reagan was (being elected to the Senate in 1964). Gerald Ford's criticism of the Vietnam War as handled by LBJ -- not sure whether that would help or hurt his chances, and as for Winthrop Rockefeller; he became Arkansas governor the same year Reagan did (1966) and I'm not sure whether he was know for much beside being Nelson's brother.
You brought up some good points about Ronald Reagan's choices for Vice-President in 1968. I am also thinking that either Senators Hugh Scott, John Sherman Cooper, Thurston Morton or Hiram Fong might have made good choices for Reagan, as all were very expreienced in politics and had served in the Senate since the 1950s.