Thanks for the helpful summary. I feel it's worth pointing out that these arguments (which seem strong!) defend only fanaticism per se, but not a stronger claim that is used or assumed when people argue for long-termism. The stronger claim being that we ought to follow Expected Value Maximization. It's a stronger ask in the sense that we're asked to take bets not of arbitrarily high payoffs, which can be 'gamed' to be high enough to be worth taking, but 'only' some specific astronomically high payoffs, which are derived from (as it were) empirically determined information, facts about the universe that ultimately give the payoff upper bounds. That said, it's helpful to have these arguments to show that 'longtermism depends on being fanatical' is not a knock-down argument against longtermism. Here's one example of that link being made: "...the case for longtermism may depend either on plausible but non-obvious empirical claims or on a tolerance for Pascalian fanaticism" (Tarsney, 2019).
I think high X-risk makes working on X-risk more valuable only if you believe that you can have a durable effect on the level of X-risk - here's MacAskill talking about the hinge-of-history hypothesis (which is closely related to the 'time of perils' hypothesis):
Or perhaps extinction risk is high, but will stay high indefinitely, in which case in expectation we do not have a very long future ahead of us, and the grounds for thinking that extinction risk reduction is of enormous value fall away.
The paper says: