Need help overcoming Shape Map rendering issue.

Hi folks.  

As per twitter thread at https://twitter.com/InsightsMachine/status/1251028978678165504 I'm having troule using a Shape Map in PowerBI due to a projection issue, and I don't have the software and/or nous to rectify.

What I want is something like this:

Yvan Richard kindly made a couple of shapemaps for me of New Zealand District Health Boards, which are here:

High-res: https://t.co/os78nV5D44?amp=1

Lower res: https://t.co/HVhAJCYxg8?amp=1

...but when I try to load them to PBI I have a projection issue, and don't have the software or nous to remedy it:

dataveld has a great article here about how to work around this using either Mapshaper or QGIS, but I didn't manage to get anywhere:

MapShaper said Unable to project -- source coordinate system is unknown

QGIS UI has changed since David's post, so I couldn't follow along past step 5. (Plus maybe this isn't even the issue, because as per screenshot the encoding bottom right looks like what the article shoots for anyways.

Can anyone help me get this into Power BI?