G'morning David, 

 DW> I wonder if they insist that the moon must be above the horizon, as
 DW> seen from the relevant place, at the exact moment of "fullness" in
 DW> order to count in the calculation. That would somewhat reduce the
 DW> frequency.

Now that you mention it,  the Herald's almanac is very precise...

    01 August {at} 0606hrs,  30 August {at} 1424hrs.

The first timing explains the month shift from July to August 
(NZST = GMT + 12hrs),  and presumably its taken at local apogee ?

 DW> I read someplace not long ago that this "second full moon in a
month"

Mmmm ... this was the last line received here - care to finish it 
off again ?

:-))
 
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