For the nerds:

Show singing is a declamatory style; there's a lot of speaking in it.

With American accents, few people notice because they're accustomed to the style.

But when you hear British, Australian or NZ accents doing the same things, it sounds more 'out-of-tune'. For example: Hugh Jackman's American is pretty good, but not flawless, so he sounds more out-of-tune than Patrick Wilson (who has also one of the best straight tones I've ever heard). -

So yeah, parlando doesn't quite cover it, but Sondheim called it 'dramatic parlando' once somewhere (the Horowitz book, I think). This is why my research points intersected: show music is all about vernacular English, and so is NZ vernacular music. Plus the showbands, and the direct influence that show music had on Maori contemporary music.