Even having lost to Helms in 1984, Hunt would have been well-positioned in 1988. Sufficiently moderate enough to represent a turn away from the old-school liberalism people wanted to disavow after the Mondale disaster, but not too far to the right in the mold of a Sam Nunn. Also, unlike Gore in 1988 he possesses real experience at this point in his career, two terms as governor rather than one incomplete Senate term.
Basically rather than running with Gore's stupid southern strategy, he competes in Iowa and New Hampshire. Perhaps he doesn't win there against the likes of Gephardt and Simon, but does respectably so that he becomes the default southern choice by the time Super-Tuesday comes around. Also, he does well with teachers unions, a critical component of Dukakis's coalition on Super-Tuesday. In the end, Dukakis doesn't make the inroads in the south he made on our actual Super-Tuesday. Instead, on Super-Tuesday Hunt holds the southern states that don't go for Jackson.
At that point he becomes the default candidate, with people weighing his national electability against Dukakis, and with people also believing Hunt is an effective compromise between Dukakis's northeastern liberalism and the DLC centrism represented at this point by people like Gore.
He could win the nomination under those circumstances easily, and then be much less vulnerable to Bush's loathsome attacks (Willie Horton, ACLU, etc.) come the fall.
Perhaps the point of departure could be that he doesn't make the race against Helms, and uses the long run-up to 1988 (technically beginning fundraising before the 1984 elections) to build a war chest and ingratiate himself with the party organizations in key states.