If you look at presidential politics after 1952, there's a tendency for the pendulum to consistently swing back and forth between the two parties. With the exception of 1980, one party will serve eight years, then the other party serves eight (Ike '53 to '61, JFK-LBJ '61 to '69, Nixon-Ford '69 to '77, Carter '77 to '81, Reagan-Bush '81 to '93, Clinton '93 to '01, Bush II '01 to '09). Reagan's victory over Carter in 1980 is the only election that disrupts this pattern, with Carter serving four and Reagan-Bush serving twelve.
Thus, I think the Democrats have the edge in 1976, regardless of who the Republican candidate is. (I'm not saying a Democratic win is a certainty. I just think the Dems have the edge.)
Assuming Agnew is still out for the bribery/tax evasion thing, there is no clear-cut Republican front runner. Nixon's candidate is John Connally, the Democrat-turned-Republican former governor of Texas. Read anything about Nixon, and you find he's absolutely mesmerized by Connally. There's no doubt Nixon would have preferred Connally to Reagan or anybody else. If Nixon is still popular in 1975 and 1976, he'd use his power to push Connally every chance he had. The question is, would Republicans go for a man who was a Democrat as recently as 1973? It worked for Willkie in 1940.
If it's not Connally, Reagan is a strong candidate for the nomination. But I don't know if Reagan could win a national election in 1976. Reagan had a reputation in 1976 as being a conservative in the Goldwater mold. Sure, he won in 1980. But in 1980, he was a challenger, able to go on the offensive against a very unpopular Democratic incumbent during a time of inflation and a hostage crisis. He wouldn't have those advantages in 1976. He'd be a perceived Goldwater conservative having to defend the mixed record of an outgoing Republican adminstration -- while his Democratic opponent goes on the offensive. Reagan became very popular later, but 1976 isn't 1980. Of course, if the Democrats nominate a lousy candidate -- which is always possible -- Reagan could win after all.
If not Connally or Reagan, the GOP nominee could be Rockefeller, Percy, McMathias, or maybe a Nixon cabinet member or Republican governor. With Agnew gone and Ford not running, you probably have seven or eight candidates. It's a free-for-all.
And it's a free-for-all among the Democrats. I agree Carter is probably not the Dem nominee. His honest outsider image doesn't resonate as much without Watergate. The same people run -- Carter, Udall, Jackson, Shriver, Bayh, Brown, Church, etc. Maybe Mondale stays in a nicer Holiday Inn and stays in the race. Maybe people who didn't run in OTL jump in after all, like Kennedy or Humphrey. (If HHH runs, Mondale doesn't.)
Bottom line: if the Democrats and Republicans nominate candidates roughly even in terms of quality, the Dems have the edge, because of the natural swing of the political pendulum. If one party nomintes a lousy candidate, the other wins.