Just plugging the feature request that would assist dramatically in this, especially in cases like Hawai’i and Aotearoa that have a colonising language and an Indigenous language that most of the endemic species names are in, even when speaking the colonising language.
For Aotearoa we’ve done the workaround that for most species that in English you would still use the Mа̄ori name, like pūkeko and kōkako, it is also listed as an English name, as in your examples. But then there are also numerous others that the Mа̄ori name and English name are both widely used in English speech and it is not so easily assigned. Until that feature request goes through, this is going to remain an issue requiring workarounds or compromises.