The New Zealand Plant Conservation Network

I note that many of the Muehlenbeckia pp are not yet completed and am uncertain about the distribution of those species you have listed as not endemic (M. australis, M. complexa and M. axillaris).

In NZ M. australis is widespread with a different form on the chatham Islands, M. complexa is throughout except on the chatham islands and M. axillaris is usually in open montane areas such as the Volcanic Plateau and throughout the tussocklands of the South island

M. axillaris gets down to the coast in the far south of the South Island as well. The photograph shows it growing on the shore with Colobanthus muelleri