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The kuhane steps ought to be around 13 nights long, because 364 / 13 = 28 and all moon calendars should have ca 28 stations. Such is the rule in the Arabic manzil calendar and also in the Chinese and the Hindu star lists (although I am aware of alternatives with minor changes in the number of 'stations'.)

Also the kuhane list has 28 stations if we count from Nga Kope Ririva Tutuu Vai A Te Taanga up to and including Ahu Akapu. Therefore the kuhane steps ought to cover on an average 13 nights. But the distance from Te Pou (if in June 30) to Hatinga Te Kohe (if September 29) is 91 nights, which should require 91 / 13 = 7 steps, not 3.

My attempt at a solution to this problem assumes there is a break in the sequence of stations somewhere between Te Pou and Hatinga Te Kohe. Such a break would be around 91 - 3 * 13 = 52 days long:

7 Te Pei 8 Te Pou 26
9 Hua Reva 10 Akahanga 26
- - 52
- -
11 Hatinga Te Koe 12 Roto Iri Are 26

The name Hatinga Te Koe could allude to absent ruling stars for 52 days.

Notably September 6 (249) is RA day 169 (= 13 * 13):

2 Alterf 4 5 6 7 (112) 8
September 2 3 4 5 6 (249)
Ca6-25 Ca6-26 Ca6-27 Ca6-28 (168) Ca7-1
tagata marama koia ra marama kua Rei te vae
Alkes (165.6), Merak (166.2) 11h (167.4)  no star listed  Al Sharas (168.6), Zosma (169.2), Coxa (169.4)
Dubhe (166.7)
March 4 5 6 7 (66) 8

By counting 13 days backwards from September 29 (272) we will arrive at Gregorian day 259 (or day 260 = 20 * 13 if we should count from December 31):

3 Dschuba 2 3 4 5 6 (124)
September 13 14 15 16 (259) 17
Ca7-8 Ca7-9 (177) Ca7-10 Ca7-11 Ca7-12
koia ki te marama tagata marama kua moe ki te ahi - e rima rave i te ika
ο Hydrae (176.1) ζ Crateris, ξ Virginis  (177.0), λ Muscae (177.1), ν Virginis (177.2) μ Muscae (177.8), 93 Leonis (178.0), Denebola (178.3) Alaraph (178.6), Phekda, β Hydrae  (179.3) η Crateris (179.9)
March 15 16 (75) 17 18 19
Saad Al Saud 5 6 (304) 7 8 9
ω Aquarii (359.2) σ Phoenicis (360.4) no stars listed π Phoenicis (363.4)

Gregorian day 260 has Sun at left in Ca7-12 drawn with a Sign in form of a vertex instead of a flame at the bottom. I think it means the creator of the C text was using the Gregorian calendar and counted from January 1 (not from December 31). RA day 180 was Gregorian day 260.

Next 13-day step backwards will bring us to Gregorian day 272 - 26 = 246, which is September 3 (see above) and Ca6-26 (where we can count 62 * 6 = 372).

This is the day before 11h when Dubhe rose heliacally. The number combination 6-26 was used in the G text at the March equinox, with Rogo in Gb6-26.

Presumably Alkes (α Crateri) rose heliacally in September 3.

272 - 39 = 233 could be close to the end of Akahanga, and my earlier guess Hanga Takaure would than hardly be correct:

An Nathra 3 4 (96)
August 19 20 (232)
Ca6-11 Ca6-12 (152)
te heheu ke - te niu kua huri ki te vai
π Leonis (150.6) 10h (152.2)
Akahanga (?)
An Nathra 5 6 7 8 (100)
August 21 22 23 24 (236)
Ca6-13 Ca6-14 Ca6-15 Ca6-16 (156)
manu teketeke ki ruga takaure kua aha te takaure i te henua ma te rima
Sadalmelik (334.6)      
 Regulus (152.7), λ Hydrae (153.2)  no star listed Simiram, Adhafera, Tania Borealis (154.7), Algieba (155.5) Tania Australis(156.0) 

Maybe there should be a central position for Hua Reva and Akahanga, in a more symmetric pattern:

7 Te Pei 8 Te Pou 26
- - 26
(11) Hua Reva (12) Akahanga 26
- - 26
(15) Hatinga Te Koe (16) Roto Iri Are 26

Possibly Hua Reva could be close to Gregorian day 272 - 52 = 220:

Murzim 2 3 4
August 5 6 7
Ca5-32 Ca5-33 Ca5-34
e vaha noho ragi erua ahi
9h (137.0)  σ² Ursa Majoris (137.6), τ Ursa Majoris (137.7), ξ Cancri (137.8) Miaplacidus (139.3)
 ω Hydrae (136.8), σ¹ Ursa Majoris (137.0), κ Cancri (137.3), Alsuhail (137.5)
Murzim 5
August 8 (220)
Ca5-35
i te hau tea
Tureis (139.8)
Murzim 6 (85) 7 8
August 9 10 11
Ca6-1 Ca6-2 Ca6-3
Erua hau tea i te henua i te rima
Markab Velorum (141.5) Al Minhar al Asad (141.6), Alphard (142.3) ω Leonis (142.6), τ¹ Hydrae (142.7), ψ Velorum (143.3),  Alterf, τ² Hydrae (143.4), ξ Leonis (143.5)

My model above for the kuhane moon stations is only an attempt to see what the whole picture could be, a way to state a problem which sooner or later has to be solved.