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If κ Sagittarii is the 'omega' star and its 'alfa' star is Gredi in Capricornus, then the question must be if there is a constellation with a last star κ just preceding Sagittarius:

Tejat Prior κ Aurigae
...
? Sagittarii κ ?
Gredi κ Sagittarii

Looking in my star list there is at least one possible answer - the constellation could be Lyra:

Akleel 12 13 Qalb al Akraab 1 2 3 (225) 4
December 23 X-mas Eve X-mas Day 26 (360) 27 28
Ca10-22 (277) Ca10-23 Ca10-24 Ca10-25 Ca10-26 Ca10-27
tupu te raau i vai oka hia te moko te marama te kava manu kara etahi te mauga pu hia
η Sagittarii (276.9), Kaus Medius, κ Lyrae (277.5) Tung Hae (277.7), Kaus Australis (278.3), ξ Pavonis (278.4) Al Athfar (278.6), Kaus Borealis (279.3) ν Pavonis (280.4) κ Cor. Austr. (280.9), θ Cor. Austr. (281.0) Vega (281.8)
June 24 25 26 27 28 29 (180)
Albatain 12 13 (40) Al Tuwaibe' 1 2 3 4
Furud (94.9), Tejat Posterior, Mirzam (95.4) Canopus (95.6), ψ1 Aurigae (95.9) no stars listed ν Puppis (99.2), ψ3 Aurigae (99.4), ψ2 Aurigae (99.5) ψ4 Aurigae (100.5)
Tejat Prior κ Aurigae
...
η Sagittarii (?) κ Lyrae (?)
Gredi κ Sagittarii

One might argue that κ Lyrae is not the last star to rise but the first star in the constellation. However, as can be seen in Hevelius' illustration - which normally shows the constellations from their back sides - the front wing of the Bird has a mirror position, is at left. The bird of Lyra has its back side towards us down on earth and therefore its last star κ is rising first.

Thus κ Lyrae could indicate the 'end station' of some great season. 277 days counted from March 21 is the day before Christmas Eve.

Here Metoro said tupu te raau i vai oka hia and the new word oka could be of help:

Oka

1. Lever, pole; to dig holes in the ground with a sharpened stick, as was done in ancient times to plant vegetables; used generally in the meaning of making plantations. 2. The four sideways poles supporting a hare paega. Okaoka, to jab, to pierce, to prick repeatedly. Vanaga.

Digging stick, stake, joist; to prick, to pierce, to stick a thing into, to drive into, to slaughter, to assassinate; kona oka kai, plantation; pahu oka, a drawer. Okaoka, a fork, to prick, to dig. Okahia, to prick. Churchill.

In G the only instance of a reversed manu rere is Gb8-5:

Gb8-3 Gb8-4 Gb8-5
no stars listed
April 26 27 28 (118)
Al Muakhar 8 9 (346) 10
ω Leonis (142.6), τ¹ Hydrae (142.7), Alterf, τ² Hydrae (143.4) ξ Leonis (143.5), A Hydrae (144.1) Ukdah (145.4)
August 11 12 13 (225)
Murzim 8 9 10 (89)
The Knot (Ukdah)