It would be nice to have additional data. However, I think we can mine the case of Ramanujan for clues about difficulty of entry. What I find striking is that he only contacted three mathematicians. Had he contacted, say, twenty before being noticed, that would have suggested a higher barrier to entry. But it was apparently just three. My own experience is that the great scientific minds are very approachable, aside from a tiny handful of scientist celebrities who understandably have to learn to be less approachable.
Recently, I gave some reasons for SIAI to begin publishing in mainstream journals, and outlined how it could be done.
I've recently been made aware of some pretty good reasons for SIAI to not publish in mainstream journals, so here they are: