One question answered: there are in fact not 30 stories per summary, consistently.

  5923 30
     3 26
     3 27
     3 28
     2 29
     1 0
     1 17
     1 19
     1 20
     1 25

Which occur on the following dates:

  2007-03-10:  29
  2007-03-24:  26
  2007-03-25:  25
  2007-05-19:  27
  2007-05-26:  26
  2007-05-28:  29
  2007-06-02:  19
  2007-06-16:  28
  2007-06-23:  17
  2007-06-24:  28
  2007-06-30:  20
  2007-07-01:  28
  2007-07-07:  27
  2007-07-15:  26
  2007-07-28:  27
  2014-01-06:  0

The 2014 instance was a site outage, discussed here: <https://news.ycombinator.com/item?id=7015129>

Spot checks suggest the others were in fact days with fewer-than-normal stories, e.g., <https://news.ycombinator.com/front?day=2007-06-30>