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The 3rd Rei could therefore be expected to also identify some major piece of Argo Navis:

APRIL 17 (107) 18 19 20 (*30) 21 22
APRIL 13 14 15 16 (*26) 17 (107)
Ga1-27 Ga1-28 Ga1-29 Ga1-30 Ga2-1
6h (91.3) ξ Orionis (92.5) Al Han'ah-4 / Maru-sha-pu-u-mash-mashu-7  FURUD (94.9) Well-22 / Arkū-sha-pu-u-mash-mashu-8
ν Orionis (91.4), θ Columbae (91.5), π Columbae (91.6)  TEJAT PRIOR (93.4), γ Monocerotis (93.5), κ Aurigae (93.6), κ Columbae (93.8) δ Columbae (95.2), TEJAT POSTERIOR, Mirzam (95.4), CANOPUS (95.6), ε Monocerotis (95.7), ψ1 Aurigae (95.9)
SOLSTICE June 23 (174) ST JOHN'S EVE
'May 24 (12 * 12) 25 26 52 * 7 = 364 28 (*68)
NAKSHATRA DATES:
OCTOBER 17 (290) 18 19 20 21 (*214)
OCTOBER 13 14 15 (288) 16 17 (*210)
Zhōngshān (274.0), π Pavonis (274.6) ι Pavonis (275.1), Polis (275.9)

MENKAR

η Sagittarii (276.9) Purva Ashadha-20
KAUS MEDIUS, κ Lyrae (277.5), Tung Hae (277.7), Shaou Pih (277.8), Kwei She (277.9) φ Oct. (278.1), KAUS AUSTRALIS (278.3), ξ Pavonis (278.4), Al Athfar (278.6)
SOLSTICE December 23 (357) CHRISTMAS EVE
'November 23 (327) 24 25 26 (*250) 27
MAY 14 15 16 (136) 17 (*57) 18 19 20
MAY 10 11 12 13 14 (*54) 15 16 (136)
Ga2-24 Ga2-25 Ga2-26 Ga2-27 (57) Ga2-28 Ga2-29 Ga3-1
φ Gemini (118.4) Drus (119.9) ω Cancri (120.2) 8h (121.7) ρ Puppis (122.0), Heap of Fuel (122.1), ζ Monocerotis (122.3),  ψ Cancri (122.6), Regor (122.7) TEGMINE (123.3) AL TARF (124.3)

RAS ALGETHI

χ Gemini (121.0), NAOS (121.3)
July 17 18 19 (200) 20 21 22 23
July 13 14 15 16 17 (*118) 18 19 (200)
SOLSTICE 'June 23 St John's Eve 25 (*96) 26 (177)
NAKSHATRA DATES:
NOVEMBER 13 14 15 16 (*240) 17 18 (322) 19
NOVEMBER 9 10 (314) 11 12 (*236) 13 14 15
ι Sagittarii (301.2), Terebellum, ξ Aquilae (301.3), Alshain (301.6), φ Aquilae (301.8) ε Pavonis, θ Sagittarii (302.3), γ Sagittae (302.5), μ Pavonis (302.7) τ Aquilae (303.8) 20h (304.4) Shang Wei (305.2), θ Sagittae (305.4), Tseen Foo (305.6), ξ Capricorni (305.8) Tso Ke (306.3) Gredi (307.2), σ Capricorni (307.5), Alshat (307.9)
η Sagittae (304.2), δ Pavonis (304.4)
January 16 17 18 (383) 19 20 21 22
January 12 13 14 15 (*300) 16 17 18 (383)
SOLSTICE 'December 23 Christmas Eve 25 (*279) 26 (360)
38 JUNE 28 29 (180) 30 (*101) JULY 1 8
ST JOHN'S EVE 25 (*96) 26 (177) 27
Ga4-16 Ga4-17 (100) Ga4-18 Ga4-19
ν Hydrae (163.1) no star listed (164)

ALTAIR

Wings-27 ANA-TIPU
η Oct. (165.4), ALKES (165.6) Merak (166.2), DUBHE (166.7)
August 31 September 1 2 3 (246)
August 27 28 (*160) 29 30 (242)
'August 4 (216) 5 (*137) 6 7
NAKSHATRA DATES:
DECEMBER 28 29 30 (364) 31 (*285)
CHRISTMAS EVE DECEMBER 25 26 (360) 27 (*281)
ι Cephei (346.0), λ Aquarii, γ Piscis Austrini, σ Pegasi (346.5) Scheat Aquarii (347.0), ρ Pegasi (347.2), δ Piscis Austrini (347.4), FOMALHAUT, τ Gruis (347.8) Fum al Samakah (348.3), ζ Gruis (348.5), ο Andromedae (348.9) Al Fargh al Mukdim-24 / Purva Bhādrapadā-26 / House-13
Scheat Pegasi, π Piscis Austrini (349.3), κ Gruis (349.4), MARKAB PEGASI (349.5)
March 2 3 4 5 (64)
February 26 27 (58) 28 (*344) March 1
'February 3 4 (*320) 5 (36) 6

However, I have in my list no prominent Argo Navis star at Rei in Ga4-17.

The Toga Nui 'Fish' changed into New Zealand (the New Sea-Land). A 'petrified fish' ought to be flat and inviting, but such was not the case, because the brothers of Maui had acted prematurely.

... When they did this, Maui had not yet reached the sacred place and the presence of the gods. Had he done so, all the male and female deities would have been appeased by the promise of portions of the fish, and Tangaroa would have been content. As it was they were angry, and they caused the fish of Maui to writhe and lash about like any other fish. That is the reason why this land, Aotearoa, is now so rough and mountainous and much of it so unuseful to man. Had the brothers done as Maui told them it would have lain smooth and flat, an example to the world of what good land should be. But as soon as the sun rose above the horizon the writhing fish of Maui became solid underfoot, and could not be smoothed out again ...

I think the myth could here refer to the outline of the keel of Argo Navis, flat like the surface of the sea at bottom but with 'mountain peaks' defining its upper border 'sky line':

 

New Zealand was divided in two great islands and so apparently was also the keel of Argo Navis. As if it had been the pair of hulls of a double canoe.

Nakshatra Fomalhaut (Mouth of the Fish) could have been the reason for the 3rd Rei.

The 4th Rei was also possible to associate with the nakshatra view, we remember:
 

JULY 10 (*112 = 7 * 16) 12 (193) 13 14
JULY 6 (*107) 7 8 9 (190) 10
Ga5-1 (111) Ga5-2 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.-16 / Shēpu-arkū sha-A-17 Phekda, β Hydrae  (179.3), η Crateris (179.9)

Deneb Cygni

93 LEONIS (178.0), DENEBOLA (178.3), ALARAPH (178.6)
September 12 13 (256) 14 (*177) 15 16
September 8 9 (*172) 10 11 12 (255)
'August 16 (*148) 17 18 (230) 19 20
NAKSHATRA DATES:
JANUARY 9 10 (*295) 11 12 13 (378)
JANUARY 5 6 7 (372) 8 9
λ Piscium (358.0), MANUS CATENATA (358.1), Alrai, θ Phoenicis (358.4), κ Andromedae (358.7) ω Aquarii (359.2), 78 Pegasi (359.5) ψ Andromedae (360.1), σ Phoenicis (360.4) γ¹ Oct. (361.4). φ PEGASI (361.7) DZANEB (362.4), γ² Oct.(362.8)
π March 15 16 (*360) 17 18 (77)
(*354 = 12 * 29) March 11 12 13 (72) π
'February 15 16 17 (48) 18 19 (*335)
JULY 15 (196) 16 (*118 = 4 * 29½) 18
JULY 11 12 (193) 13 (*114 = 6 * 19) 14
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 18 (261 = 9 * 29) 19 20
September 13 (256) 14 (*177 = 6 * 29½) 15 16
'August 21 22 (*154) 23 24 (236)
NAKSHATRA DATES:
JANUARY 14 15 16 17 (382)
JANUARY 10 11 12 13 (378)
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 Octantis (364.4) Al Fargh al Thāni-25 Uttara Bhādrapadā-27 / Wall-14
0h (365.25)
Caph, SIRRAH (0.5), ε Phoenicis (0.8) ALGENIB PEGASI (1.8)
March 19 (78) 20 EQUINOX 22
March 15 16 (*360) 17 18 (77)
(*336 = 12 * 28) 'February 21 (52) 22 TERMINALIA

I think the Rei type of glyph could refer to the dark Winter Fish who at Dawn changed into a solid (frozen, petrified) Fish of Summer - the stars were no longer easy to observe and nothing would change as long as the Sun blinded the astronomers.