Rawls and rationally intractable disagreement

Let me preface by saying I am not a political philosopher, and this may be off-base. Start by granting this claim for the sake of the argument:

1. The disagreement between comprehensive views is very long-standing and there is no progress to agreement, except when non-rational, coercive methods are applied to generate agreement or for other merely sociological reasons there happens to be cultural homogeneity.

(I don't know how to characterize merely sociological reasons.) Now consider two possible explanations of (1):

2. People's idiosyncratic or culturally-based preferences, as well as their presently-held comprehensive views, often significantly bias them in their disagreements between comprehensive views.
3. It is not possible to resolve the disagreement between comprehensive views by reason alone.

We now have at least three options: only (2) explains (1); only (3) explains (1); both (2) and (3) explain (1). How would we decide between these? Well, first observe that (2) is a truism. Moreover, (2) clearly is at least a part of the explanation of (1). So of the three options, the two that remain are:

• both (2) and (3) explain (1)
• (2) by itself explains (1)

I understand that it is important to Rawls' project that (3) be a part of the explanation of (1), because it is important to Rawls' project that (3) be true, and apparently the main evidence he adduces for (3) is that it explains (1).

But now the question whether (1) is explains by (2) and (3), or simply by (2), is to a significant degree an empirical question.

And there is an obvious experiment to test between these options. Take a bunch of intelligent and rational people without idiosyncratic and culturally-based preferences who do not adhere to any comprehensive views, and see if they come to agree to on a comprehensive view or against all of them--if they do, then (3) is not a part of an explanation of (1), and if they don't, then (3) is a part of an explanation of (1). And we cannot at present rule out the possibility that such an experiment would rule in favor of the hypothesis that (2) by itself explains (1).

But now note that this experiment is precisely the original situation of deliberation under the veil of ignorance. And note that we can say directly this. If it is an empirically open possibility that agreement on a comprehensive view or against all of them would arise in the original situation, then it seems to be an open possibility that the delegates would legislate in accordance with a comprehensive view or in ways that significantly impugn the freedom to follow comprehensive views. And that's unacceptable to Rawls.

Sound-bite version: Please don't infer that a debate would be unsettled in an idealized situation from the fact that it's unsettled in the real world.

But I probably don't know what I'm talking about.