I went back to the early records and included all of the storms from the U.S. Weather Bureau era with 70 or more six-hour position points (including a few in the later years that I had missed). Here is the restructured list:

NONAME - Aug/Sept, 1893 - 70
NONAME - June, 1934 - 70
NONAME - Sept, 1947 - 70
DOG - Aug/Sept, 1950 - 70
BEULAH - Sept, 1967 - 70
BERTHA - July, 2008 - 70 (didn't make the top 10, but certainly made the Longevity list)
NONAME - Sept, 1926 - 71
NONAME - Sept, 1936 - 71
FRAN - Aug/Sept, 1996 - 71
NONAME - Aug/Sept, 1930 - 72
EDOUARD - Aug/Sept, 1996 - 73
IVAN - Sept, 2004 - 73
NONAME - Aug, 1915 - 74
NONAME - Aug/Sept, 1906 - 75
DORA - Aug/Sept, 1964 - 75
MARILYN - Sept/Oct, 1995 - 75
MITCH - Oct/Nov, 1998 - 76
ALBERTO - Aug, 2000 - 78
NONAME - Aug/Sept, 1900 - 80
INEZ - Sept/Oct, 1966 - 81
ARLENE - Aug, 1987 - 81
NONAME - Sept/Oct, 1893 - 83
NONAME - Aug, 1899 - 85
KYLE - Sept/Oct, 2002 - 89
CARRIE - Sept, 1957 - 91
INGA - Sept/Oct, 1969 - 99
GINGER - Sept/Oct, 1971 - 118

The record for a 'July only' storm appears to be CLAUDETTE in 1979 with 57 bulletins, however, given the 70 for the storm in June, 1934, I'm not sure of the significance. Note that there was an un-named storm in July/Aug, 1909 with 60. At the other end of the season there was a Nov/Dec storm in 1888 with 63. Bertha 2008 would need to track for an additional 10 full days in order to make the top ten on the list - but I suppose that it could happen.
Cheers,
ED