Maybe you are seeing something here that I am not. The only solution I have found in solving the social objectivity problem is to not form a social construct and not lend/give authority to it. This leaves each individual to the maximum liberty and preferences in subjective values, and unbinds everyones governance from everyone else.

So I would say the solution is to recognize Individual Sovereignty, that holds no subservience to any social construct, but recognizes individual self ownership as the dominate construct, an individual construct.

In this way the truth component of social objectivity is uncoupled, and negotiated person to person.

There is the other problem when state construction occurs, that there is no limiting factor that the social construct will ever maintain recognition of individual constructs. This leads repeatedly to escalation into various factions weaponizing whatever state constructs there are, to a preferred factional social objectivity.

When you build a state, you build the problem of social objectivity.