The sooty back of manu tara refers to her past. In the journey of Moon she has met Sun. In her dark phase, in the position between earth and sun, she has bathed in his rays. It is therefore not strange to find soot on her back, it is the telltale evidence of her encounter with Sun, the 'fire' in the sky.

The white back of kena also refers to her past, because the full moon white (kuokuo) phase of Moon ended at Hanga Kuokuo:

Full Moon
14 hatu ngoio a taotao ika.
15 ara koreu a pari maehaeha.
16 hanga kuokuo a vave renga.
The Tree
17 Opata roa a mana aia.
18 vai tara kai u(a) a ngao roaroa a ngao tokotokoa.
19 hia uka a hakairiiri a hakaturuturu.
20 hanga ohiro a pakipaki renga. kena

We can conclude that the map of the island described by the 2nd list of place names probably describes the path of Moon. The first half of the list of bird names covers 8 stations along this path, from item 13 (Cabo Norte, manu tara) to item 20 (Hanga Ohiro, kena), corresponding to the redmarked nights below in the Hawaiian calendar:

1 Hilo 7 Ole-ku-kahi 14 Akua 21 Ole-ku-kahi 26 Kane
2 Hoaka 8 Ole-ku-lua 15 Hoku 22 Ole-ku-lua 27 Lono
3 Ku-kahi 9 Ole-ku-kolu 16 Mahea-lani 23 Ole-pau 28 Mauli
4 Ku-lua 10 Ole-pau 17 Kulu 24 Kaloa-ku-kahi 29 Muku
5 Ku-kolu 11 Huna 18 Laau-ku-kahi 25 Kaloa-ku-lua
6 Ku-pau 12 Mohalu 19 Laau-ku-lua
  13 Hua 20 Laau-pau

Spica (Ana-roto) could be the star of manu tara. Roto means inside, and indeed Cabo Norte is about halfway between the prow Rano Kau and the stern Rano Raraku. The path of Moon goes from west to east and manu tara announces the return of light in early spring. The beginning of spring is between winter and summer.

Roto

1. Inside. 2. Lagoon (off the coast, in the sea). 3. To press the juice out of a plant; taheta roto pua, stone vessel used for pressing the juice out of the pua plant, this vessel is also just called roto. Roto o niu, east wind. Vanaga.

1. Marsh, swamp, bog; roto nui, pond; roto iti, pool. 2. Inside, lining; o roto, interior, issue; ki roto, within, into, inside, among; mei roto o mea, issue; no roto mai o mea, maternal; vae no roto, drawers. Churchill.

North of the equator Spica will rise heliacally in autumn, and 13h 23 is about 20 days beyond autumn equinox.

1

Ana-mua, entrance pillar

Antares, α Scorpii

-26° 19'  16h 26

3

Ana-roto, middle pillar

Spica, α Virginis

-10° 54'  13h 23

South of the equator Spica will rise heliacally about 20 days beyond spring equinox, around 'April 10'. Is that the time of manu tara? Antares will come around 3h / 24h * 12 = 1½ month later, i.e. about 'May 25', which could announce the beginning of summer. April/May is the time when the Pleiades apparently were invisible (cfr at maitaki):

30-40 days invisible April/May Matariki i raro
heliacal rising June
start for ritual calendar July
rising in the evening November Matariki i nika
new year November/December

The 'sinking canoe' could refer to how the prow disappears in April/May.

When the Pleiades once again appears in the sky they could come with summer, rise with Sun. At Anakena a new king is born. The season of white Moon is in the past and therefore the kena birds have white backs. But April/May is not 'April' / 'May'. It is 'October' / 'November', i.e. when the Pleiades are invisible winter solstice lies ahead and the prow of the canoe is going down.

When Antares rises heliacally around 'May 25' it means around October 25 and Ana-mua could be Rei-mua, the prow of the canoe, and summer solstice lies ahead.

Spica around 'April 10' means around October 10. Number 13 (Hua, Ko te hereke a kino ariki) indicates how the Sun King has a bad time. Manu tara is, though, a good sign - like the swallow who on the prow of the Pharaoh canoe in the Underworld is pointing ahead (cfr at vaha kai):

Maybe the swallow of the 'sea' (manu tara) has swallowed the soul of Sun in order to protect him from the waters of the Underworld.