Cross-over voting in primaries -- primordial soup for moderates?

I've long had the impression that Senator John Warner owes his longevity in the Senate to a primary system that allows cross-over votes. Democrats and liberals often crow that they vote for Warner in Republican primaries to ensure Republicans can't nominate a more conservative candidate.

Got me to wondering -- doeds anyone know how to determine if the other 7 senators involved in the filibuster compromise are products of similar primary systems?