If you want better politicians, there are two things you can do:
Vote in primaries, there are different rules about this but if it means you have to join and participate in party activity to vote for a candidate then so be it.
hold them accountable together as ironic as it is: as a lobbying group, or even more grandiose work together with as many citizens of the state (even across the party line, no craziness though), to hold the governor/politician accountable.