Most likely POD for HHH in 1968 is imo Reagan getting it because Nixon decided to play the long game and wait till 72 or 76.
My guess is you get a few potential scenarios 1) HHH wins in 72, gets to set things up for Muskie or Carter in 76 2) HHH wins in 72, but things get botched enough you get a republican(Reagan/nixon/bush your choice) in 76 2) Nixon wins in 1972("Third time's the charm for Tricky Dick...).
The least likely but theoretically doable one would be Reagan in 1972 with it's own variations -- On one hand you have expanded welfare(UBI, UHC, more generous than OTL EITC), vietnam being a stalemate, 4-6 liberal justices on the SC with resuting court cases, expansion of busing for 4 more years causing a backlash. OTOH there's the fact that Reagan's going to be elected in stormy waters, so either 4 or 8 years of him with the end results being as I keep mentioning weaker movement conservatism -- someone did a thread on 1968 Reagan on here with that result but i forget who.