Hanga Pau Kura seems to be named Hanga-poukura on the map above. Although Barthel does not equate Hanga Pau Kura with Hanga Te Pau, I think the names and the general location is leading us to conclude it ought to be the same place: 'The canoe of the explorers lands on the shore below Vinapu at Hanga Te Pau' (The Eighth Island, p. 69). A map from Alfred Métraux, Ethnology of Easter Island, locates Vinapu for us:

According to the first of the maps above the high and steep coastline ends where Hanga-poukura is located, i.e. it is should be the natural harbour for someone wishing to reach Vinapu. But according to the more detailed map of Métraux Hanga-paukura is located more to the east. And pau is definitely not equal to pou, rather its opposite. We must look out of wordplays.

Yet, the information of Barthel does not make sense. It is not possible to locate Hanga Te Pau below Vinapu and at the same time put it between Hanga Pau Kura and Vaihu. The difficulty may be due to a misconception - Hanga Te Pau is not located in the normal geography of the island, it is a place in time.

Pau is the key word, and it is probably alluding to Puna Pau (cfr top left on the first map):

Pau

1. To run out (food, water): ekó pau te kai, te vai, is said when there is an abundance of food or water, and there is no fear of running out. Puna pau, a small natural well near the quarry where the 'hats' (pukao) were made; it was so called because only a little water could be drawn from it every day and it ran dry very soon. 2. Va'e pau, clubfoot. Paupau: Curved.

1. Hakapau, to pierce (cf. takapau, to thrust into). Pau.: pau, a cut, a wound, bruised, black and blue. 2. Resin. Mq.: epau, resin. Ta.: tepau, gum, pitch, resin. (Paupau) Hakapaupau, grimace, ironry, to grin. 3. Paura (powder), gunpowder. 4. Pau.: paupau, breathless. Ta.: paupau, id. 5. Ta.: pau, consumed, expended. Sa.: pau, to come to an end. Ma.: pau, finished. 6. Ta.: pau, to wet one another. Mq.: pau, to moisten.

The basic idea seems to be 'finished' (out of breath, out of water). Thus Hanga Te Pau could mean the harbour at the end of the journey. The last words on page 17 are he vari ki hanga.te pau:

this is Te Pito O Te Kainga, which also received its name from the dream soul.	ko te pito o te kainga i nape ai e toona kuhane.	p. 17
The canoe continued its exploration and in a sweep sailed on to Hanga Te Pau.	hokoou.he rarama he oho te vaka he vari ki hanga.te pau
They went ashore and took the food with them.	he tomo ki uta.he too i te kai ki uta.
		p. 18
They pulled the canoe onto the beach and left it there.	hee totoi i te vaka ki uta he hakarere.

Vari means a curve and also paupau means a curve. Possibly a curve is a sign of approaching end. Old people no longer have straight backs.