You might be interested to compare the Hauksbók version of this
chapter, which Jones translated:

http://www.heimskringla.no/original/islendingesagaene/eirikssagarauda.php

Pretty much the same story, but a lot of differences in wording in
this chapter. This one too has a recap of the dire situation after
Bjarni's suggestion:

Þetta þótti öllum svá drengiliga boðit, at engi vildi móti mæla. Gerðu
þeir svá, at þeir hlutuðu mennina, ok hlaut Bjarni at fara í bátinn ok
helmingr manna með honum, því at bátrinn tók ekki meira.