I think this line of thinking is productive. Other thoughts:

For cooperative agents to thrive among non-cooperators, they must be able to identity other cooperators. Of course you can wait for the non-cooperators to identity themselves (via an act of non-cooperation in tit-for-tat, or a costly signal), but other agents are inevitably going to rely on other heuristics and information to predict the hidden strategies of others, and, when the agents are human, they will do this in a risk-averse way.

Accordingly, a low-trust society (one in which no single entity is able or willing to enforce cooperative behavior over all individuals) is seldom homogeneously low-trust (or low trustworthiness), but rather a amalgamation of subgroups, each of which is relatively more trusting and trustworthy, but only within the subgroup. Because of the need to guess at the hidden strategies of others, these subgroups don't necessarily split the society into "levels of trustworthiness".

The task of moving to a high trust/trustworthiness society becomes the task of getting cooperative subgroups to identity other potentially cooperative subgroups, and for those two subgroups to figure out a way to share the duty of enforcing cooperative behavior, or of allowing more true information about the cooperative behavior of individuals to flow between groups.

Since evolution produces a special cooperation in close-kinship relations, the simplest artificial grounds for merging two previously uncooperative subgroups is to stretch the kinship relation as far as possible (as in clans, or any society where third- and fourth-cousin relationships are considered relevant).

Some other examples related to this process:

• The spread of shared religious identity (when this involves submitting to a punitive religious law).
• Trade unions, cartels and guilds.
• Language boundaries (which impede information about trustworthiness from flowing across groups).
• Race, (as an amalgam of language, religion, class etc packaged with a convenient visual ID)
• The cultivation of national and class identities.
• The oft-maligned internal division of political parties, which smash together otherwise separate subgroups.
• The forcible crushing of the old markers of old subgroups (old religions, old kinship practices, old languages)

It's a bit of theory of everything, but I think this is a helpful framing.