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There are 12 more stars which have been assigned Greek letters in Piscis Austrinus:

ι 21h 44m 56.79s 21h 44.947m 330.4
θ 21h 47m 44.17s 21h 47.736m 331.1
η 22h 00m 50.22s 22h 00.837m 334.4
μ 22h 08m 22.95s 22h 08.383m 336.3
υ 22h 08m 25.93s 22h 08.432m 336.3
τ 22h 10m 08.48s 22h 10.141m 336.8
λ 22h 14m 18.74s 22h 14.312m 337.8
β 22h 31m 30.29s 22h 31.505m 342.2
ε 22h 40m 39.33s 22h 40.656m 344.5
γ 22h 52m 31.56s 22h 52.526m 347.5
δ 22h 55m 56.89s 22h 55.948m 348.4
Fomalhaut 22h 57m 38.83s 22h 57.647m 348.8
π 23h 03m 29.76s 23h 03.496m 350.3
Saad Al Thabib 3 4   5 (275)
February 13 (409) 14 (45) 15
Ca12-13 (329) Ca12-14 Ca12-15
oho te vae te vai okahia te henua
Azelfafage, κ Capricorni (328.7), Enif, Erakis (329.2), 46 Capricorni (329.3), ι Piscis Austrini (329.4) λ Capricorni (329.6), ν Cephei (329.7), Deneb Algiedi (329.8), θ Piscis Austrini (330.1) Kuh (331.4)
August 15 16 (228) 17
Murzim 12 13 (92) An Nathra 1
Ras Elaset Australis (146.6) Vathorz Prior (147.9), υ¹ Hydrae (148.4) Ras Elaset Borealis (148.7)
Saad Al Thabib 6 7 (277)
February 16 17 (413)
Ca12-16 Ca12-17 (333)
oho te vae kua pure ia
no stars listed η Piscis Austrini (333.4)
August 18 19 (231)
An Nathra 2 3 (95)
 Tseen Ke (149.9), ν Leonis (150.1) π Leonis (150.6)
Saad Al Thabib 8 9 10 (280)
February 18 19 (50) 20
Ca12-18 Ca12-19 Ca12-20 (336)
oho te vae koia ra kua haga hia kua moe
Kae Uh (334.0), Al Kurhah (334.4) 22h (334.8) τ Piscis Austrini (335.8), ζ Cephei (336.2), λ Cephei (336.3)
Sadalmelik (334.6), ι Aquarii (334.7), Alnair (335.1), μ, υ Piscis Austrini (335.3)
August 20 21 22 (234)
An Nathra 4 5 (97) 6
10h (152.2) Regulus (152.7), λ Hydrae (153.2) no star listed
υ² Hydrae (151.8), Al Jabhah (152.4)
Saad Al Thabib 11 12 13 14 15 (285)
February 21 22 23  24 25 (56)
Ca12-21 Ca12-22 Ca12-23 (339) Ca12-24 Ca12-25
te niu ku hakatu ua te maitaki - kupega tuku hia mai mata hakatuu te vae paupau te niu tutuu
λ Piscis Austrini (336.8), ε Cephei (337.2), Ancha (337.4) ρ Aquarii (338.2) Sadachbia (338.6), π Aquarii (339.5) ρ Cephei (340.2), ζ Aquarii (340.4), Alrediph (340.5) σ Aquarii (340.9), Homan, β Piscis Austrini (341.2)
August 23 24 (236) 25 26 27
An Nathra 7 8 9 (101) 10 11
Simiram, Adhafera, Tania Borealis (154.7), Algieba, q Carinae (155.5) Tania Australis (156.0) μ Hydrae (157.1) no star listed Shir (158.9), p Carinae (159.3)
  Saad Balaa 1 2
26 (422) 27 (58)
Ca12-26 Ca12-27
oho te rima o te niu a hagahaga
υ Aquarii (341.9), η Aquarii (342.1) Situla (342.7), ε Piscis Austrini (343.5)
August 28 (240) 29
An Nathra 12 13 (105)
φ Hydrae (160.3) no star listed
Saad Balaa 3 (288)   Leap night   4
February 28 (59) 29 (425) March 1
Ca13-1 (344) Ca13-2 Ca13-3
Kua haga te tagata kua haga e kua noi
Matar (344.2) Leap night no star listed
Saad Balaa 5 6 7 (292)
March 2 3 (63) 4 (429)
Ca13-4 Ca13-5 (348) Ca13-6
tagata ma te kihikihi koia ra kua oho
τ Aquarii (345.7), ι Cephei (346.0), γ Piscis Austrini (346.5) λ Aquarii (346.5), Scheat Aquarii (347.0), δ Piscis Austrini (347.4) Fomalhaut (347.8)

The first star (ι) rose heliacally in February 13 (409) at the first oho te vae glyph and the 12th star (Fomalhaut) rose in March 4. I guess the mouth depicted in Ca12-17 could refer to the Mouth of the Fish (Fom-a-Haut), especially so as it is drawn upside down. But maybe it refers to the constellation rather than to α.

Or else they saw the Southern Fish not only upside down but also reversed, as a Sign of the final of the old year. Day 413 = 14 * 29½ could have been the reason why η was chosen instead of α.

The last star - appropriately the 'portal of exit' (π) - rose with the Sun in March 5

Saad Balaa 8 (293)
March 5 (65)
Ca13-7 (350)
manu rere
Scheat Pegasi, π Piscis Austrini (349.3), Markab Pegasi (349.5)

Glyph 350 comes after the leap day (February 29) and therefore its RA day number is 1 less (349) than the glyph number, because I have guessed the stars were mapped by using a year with 365¼ days.

23h is consequently in day 23h / 24h * 365¼ + 1 = 351.0 (March 6) instead of in day 350.0 (March 5), as in a regular year. March 5 can be written as 3-5 and this number can in turn be thought of as a short version of 350 (= 15 days left of the old year).