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I suppose we should not bother too much about the position of heliacal Sirius at the time of Haedus II until we reach June 30 - its position at the time of rongorongo. Up until that time the dates of rongorongo ought to have determined the way the glyphs were designed.

But the text seems to call the attention of the reader around 75 days later:

72
Ga2-5 Ga2-6 Ga2-7 (37) Ga2-8
ν Puppis (99.2), ψ3 Aurigae (99.4), ψ2 Aurigae (99.5)

Gemma

ψ4 Aurigae (100.5), Mebsuta (100.7) Sirius (101.2), ψ5 Aurigae (101.4), ν Gemini (101.6), ψ6 Aurigae (101.7) τ Puppis (102.2), ψ7 Aurigae (102.4)
June 28 29 30 (181) July 1
●JUNE 29 SIRIUS (181) ●JULY 1 2 3 (*104)
Ga5-1 (111) 7 * 16 = 8 * 14 Ga5-3 Ga5-4 Ga5-5
θ Crateris (175.0), υ Leonis (175.2), ω Virginis (175.3), ι Crateris (175.5) ο Hydrae (176.1) ζ Crateris, ξ Virginis  (177.0), λ Muscae (177.1), ν Virginis (177.2), μ Muscae (177.8) Al Sarfah-10 / Uttara Phalguni-12 / Zibbat A.-17 / Shēpu-arkū sha-A-18 Phekda, β Hydrae  (179.3), η Crateris (179.9)

Deneb Cygni

93 Leonis (178.0), DENEBOLA (178.3), ALARAPH (178.6)
September 12 16 * 16 14 15 16
NAKSHATRA DATES:
●DECEMBER 29 30 (*284) 31 ●JANUARY 1 2
λ Piscium (358.0), MANUS CATENATA (358.1), Alrai, θ Phoenicis (358.4), κ Andromedae (358.7) ω Aquarii (359.2) ψ Andromedae (360.1), σ Phoenicis (360.4) φ Pegasi (361.7) Dzaneb (362.4)
π March 15 16 (75) 17 18
●JULY 4 5 (186) 6 (*107) 7 (¤7)
Ga5-6 Ga5-7 Ga5-8 (118) Ga5-9
no star listed (180) π Virginis (181.0), θ Crucis (181.5) 12h (182.6) Alchita, Ma Wei (183.1), Minkar (183.7), ρ Centauri (183.9)
ο Virginis (182.1), η Crucis (182.5)
September 17 (260) 18 19 20 (*183)
NAKSHATRA DATES:
●JANUARY 3 (368) 4 5 6 (¤190)
η Tucanae (363.0), ψ Pegasi (363.1), 32 Piscium (363.2), π Phoenicis (363.4), ε Tucanae (363.6), τ Phoenicis (363.9) θ Oct. (364.4) Al Fargh al Thāni-25 Uttara Bhādrapadā-27 / Wall-14
0h (365.25)
Caph, SIRRAH (0.5), ε Phoenicis, γ³ Oct. (0.8) ο Oct. (1.3), ALGENIB PEGASI (1.8)
March 19 20 (*364) 21 22 (446)

When on Easter Island (and in rongorongo times) the Sun rose with the first stars of Raven it meant spring equinox was around the corner. I therefore think the glyphs could still be read without bothering about where Sirius had been in the past.

But possibly a change was due around 10 days after Ga5-1:

●JULY 8 (¤8) 9 (190)
Ga5-10 Ga5-11 (121)
Pálida (184.6), Megrez (184.9) Hasta-13 / Chariot-28
GIENAH (185.1), ε Muscae (185.2), ζ Crucis (185.4), Zaniah (185.9)
September 21 (264) EQUINOX
NAKSHATRA DATES:
●JANUARY 7 (372) 8 (¤192)
χ Pegasi (2.1), θ Andromedae (2.7) σ Andromedae (3.0), ζ Tucanae (3.5), ρ Andromedae, π Tucanae (3.7)
March 23 (¤266) 24 (448)

The Sun had here passed the first of the stars in the beams of the Southern Cross, viz. Pálida (the pale one, δ):

This strangely less bright of the 4 could have been depicted as such on the Gateway of the Sun:

... Schematic drawing of the 'socle of the central figure of the Sun Door' on which can be seen the 'eyes' with 'Star' signs on the coronas and the 'ring nose' as in the position of the constellation Southern Cross at nightfall at the solstices ...

As if by coincidence Pálida rose with the Sun in day 184 after 0h and in the following day came the southern spring equinox - a week after the double Babylonian ecliptic stations where Leo went away.

I have always wondered what creature was sitting at the rear end of the Sun ship in the night of Nut:

Now I know, because Wikipedia has a kind of glyph dictionary:

The rear end (muri) of the Lion was cut off from his front part and only the rear end went safely across the waters of the night. Perhaps his rear end was twisted around: