Please pardon my prying,

No problem, and I welcome more such questions.

but as you've spent more time with SIAI, have you seen tendencies toward this sort of thing? Public declarations, competitions/pressure to prove devotion to reducing existential risks, scolding for not towing the party line, etc.

No; if anything, I see explicit advocacy, as Carl describes, against natural emergent fanaticism (see below), and people becoming less fanatical to the extent that they're influenced by group norms. I don't see emergent individual fanaticism generating significant unhealthy group dynamics like these. I do see understanding and advocacy of indirect utilitarianism as the proper way to 'shut up and multiply'. I would be surprised if I saw any of the specific things you mention clearly going on, unless non-manipulatively advising people on how to live up to ideals they've already endorsed counts. I and others have at times felt uncomfortable pressure to be more altruistic, but this is mostly pressure on oneself — having more to do with personal fanaticism and guilt than group dynamics, let alone deliberate manipulation — and creating a sense of pressure is generally recognized as harmful.

I've seen evidence of fanaticism, but have always been confused about what the source is (did they start that way, or were they molded?).

I think the major source is that self-selection for taking the Singularity seriously, and for trying to do something about it, selects for bullet-biting dispositions that predispose towards fanaticism, which is then enabled by having a cause and a group to identify with. I don't think this is qualitatively different from things that happen in other altruistic causes, just more common in SIAI due to much stronger selective pressure for bullet-biting.

I also have the impression that Singularitarian fanaticism in online discussions is more common among non-affiliated well-wishers than people who have spent time with SIAI (but there are more of the former category, so it's not easy to tell).