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6. In June 1 (says Allen) is Antares rising at sunset. This statement is in fairly good agreement with the information in Wikidpedia:

... Antares is visible in the sky all night around May 31 of each year, when the star is at opposition to the Sun. At this time, Antares rises at dusk and sets at dawn ...

Antares rising in the east at sunset:
Ga1-7 Ga1-8 Ga1-9 Ga1-10 Ga1-11
'May 31 'June 1 (152) '2 '3 '4
"March 29 "30 (89) "31 "April 1 "2
Culmination at midnight of Antares:
Ga2-14 Ga2-15 Ga2-16 Ga2-17 Ga2-18
7h (106.5) 'July 8 '9 '10 '11 (192)
"May 5 "6 "7 "8 "9 (129)

The distance from June 1 to July 11 is 192 - 152 = 40 days. But the text seems to add 36 days, the distance from June 1 to July 7:

Ga2-12 Ga2-13 Ga2-14 Ga2-15 Ga2-16
'July 5 '6 7h (106.5) '8 '9
"3 "4 "May 5 (125) "6 "7

Here mago comes in the center between the twins Ga2-12 and Ga2-16.

Perhaps we ought to read the glyphs in groups of 7, in weeks:

Antares rising in the east at sunset: 30
Ga1-7 Ga1-8 Ga1-9 Ga1-10 Ga1-11
'May 31 'June 1 (152) '2 '3 '4 (155)
"March 29 "30 (89) "31 "April 1 "2
35 = 5 weeks
Culmination at midnight of Antares:
Ga2-12 Ga2-13 Ga2-14 Ga2-15 Ga2-16 Ga2-17 Ga2-18
'July 5 (186) 6 7h (106.5) 'July 8 '9 '10 '11
"3 "4 "May 5 "6 "7 "8 "9