Perhaps a step forward would be for disputants to publicize their probability estimates and update them as the conversation proceeds.

Would that be desirable? I know, for example, that when reading Robin's posts on that topic I often updated away from Robin's position (weak arguments from a strong debater is evidence that there are not stronger arguments). Given this possibility, having public numbers diverging in such a way would be rather dramatic and decidedly favour dishonesty.

In general there are just far too many signalling reasons to avoid having 'probability estimates' public. Very few discussions even here are sufficiently rational as to make those numbers beneficial.