Like most majoritarian arguments, this throws away information: the relevant reference class is "mainstream beliefs you think are that improbable".

No, that is the reference class intended and described ("apparently overwhelming evidence").

In that class, it's not obvious to me that one would certainly be wrong more than once, if one could come up with 10^20 independent mainstream propositions that unlikely and seriously consider them all while never going completely insane.

Your prior is wrong (that is, it does not reflect the information that is freely available to you).

Going completely insane in the time required to consider one proposition seems far more likely than 10^-20, but also seems to cancel out of any decision, so it makes sense to implicitly condition everything on basic sanity.

Considering normal levels of sanity are sufficient. Failing to account for the known weaknesses in your reasoning is a failure of rationality.

I'd be inclined to accuse anyone going above... something below 10^-7... of being far too modest.

I am comfortable accusing you of being confused about probabilities as related to human beliefs.