I think the answer may be that the difference in political systems (parliamentary vs presidential) and party systems (less two-party but with greater party discipline) solves many of the problems term limits are intended to solve in completely different ways.
Maybe a better answer would be for US states to adopt the parliamentary system? Although there is some debate about what the "republican form of government" clause means, it arguably doesn't rule out parliamentary republicanism, and Luther v Borden (1849) ruled the clause wasn't justiciable anyway. Added to that, the widespread practice in first half of the 19th century, in which governors were elected by state legislatures, was de facto the parliamentary system. I don't think there is any federal constitutional obstacle to trying this – it is just a political culture issue, it currently sits outside the state constitutional Overton window.
While you could adopt the Australia/Canada model of a figurehead state governor/lieutenant governor with a state premier, I think just having a premier but calling them "the governor" would be more feasible