Max, my NZ connection told me that the two languages originated in the same area. (What he based this on, I don't know.) Interestingly, he said he gets Maori words by studying the vowel structure. I don't speak or read Hawaiian, but I know it is a language brimming with vowels.
He taught me how to pronounce Aotearoa. One of the Hawaiian islands is Oahu: three syllables!