I guess I’ve always lumped the country-club folks with the managerialists. Whatever the case, I’d be inclined to include libertarians in your breakdown of the factions.
And regarding those libertarians, let’s just say I’m not quite as optimistic that the abstract principle that you’ve noted will serve as sufficient glue. My general sense is that the great bulk of libertarians take their position on government not primarily on the basis of a theory that compartmentalizes the sources of power in a society, but because they believe that removing morality from government will mean that they will never have to pay attention to others’ declarations about morality.
More broadly applicable than my impression, however, is that libertarians don’t see the secular philosophy as “you must honor a contract because the state says so.” The state is not the source of the coercive power. Rather, they see, as you admit, that one “of the few proper roles for government that most libertarians agree upon is enforcement of contractual arrangements freely entered,” and they would say that a person must honor those contracts because the state will enforce an explicit penalty (e.g., fines or jail time). No external morality is necessary for such a system except the narrow morality of immediate self-interest.