Realistic epistemic expectations

A lot of communication is about explaining what you mean, not about proving that something is true. In many cases, you don't need to provide any evidence at all, as it's already available or trivially obtainable to your audience, the bottleneck is knowing what to look for. So it may well be sufficient to give a bit of motivation to keep them learning (such as the beauty of the concepts, or of their presentation). The evidence about truth of the eventual conclusions, or clear idea of what they are, could remain irrelevant throughout.

If I were to restrict myself to making claims that I could substantiate in a mere ~2 hours, that would preclude the possibility of me sharing the vast majority of what I know.

Using your mathematical analogy, would it help to explicitly assume a few plausible lemmas whose proof can be given later, and derive your main result from them, in order to cut down on the size of the post?

One approach I've been working with is sharing models rather than arguments. For example, nbouscal and I recently debated the relative importance of money for effective altruism. It turned out that our disagreement came down to a difference in our models of self-improvement: he believes that personal growth mostly comes from individual work and learning, while I believe that it mostly comes from working with people who have skills you don't have.

Any approach that started with detailed arguments would have been incredibly inefficient, because it would have taken much longer to find the source of our disagreement. Starting with a high-level approach that described our basic models made it much easier for us to hone in on arguments that we hadn't thought about before and make better updates.

I used to have an adage to the effect that if you walk away from an argument feeling like you've processed it before a month has passed, you're probably kidding yourself. I'm not sure I would take such a strong line nowadays, but it's a useful prompt to bear in mind. Might or might not be related to another thing I sometimes say, that it takes at least a month to even begin establishing a habit. While a perfect reasoner might consider all hypotheses in advance or be able to use past data to test new hypotheses, in practice it seems to me that being on the lookout for evidence for or against a new idea is often necessary to give the idea a fair shake, which feels like a very specific case of noticing (namely, noticing when incoming information bears on some new idea you heard and updating).

In general, when a position is non-obvious, a single conversation is nowhere near enough time to convince a rational person that it's very likely to be true.

Oh, the situation is much worse than that. If your claim is empirical, and needs many background claims to even be coherent, then the evidence required may far exceed what any one person could gather. Compare the claim that one gene with a silly name controls the expression of another - consider the amount of evidence needed to justify the jargon in that case.