I still consider automatic blockers to be about obviousness (not
criticality), but I'm open to different resolutions here anyway, if we
want to come up with something really clear.

For the record, we talked about this yesterday in QA meeting [1], and the majority opinion was that last minute blocker policy is applicable to automatic blockers. Adam promised to slightly clarify that in the SOP.

[1] search for "Automatic blockers vs. 'last minute' blockers" at https://meetbot.fedoraproject.org/teams/fedora-qa/fedora-qa.2019-09-16-15.01.log.html