Hi Sean,
I managed to get mine sorted.
I had set my tiling scheme to 'use existing cached map/image service' and selected the ESRI 'NZ Dark Canvas' basemap that is available in ArcOnline (in order to control and set my projection as NZTM). As it turns out, this tiling service uses a JPEG tile format which I didn't notice until looking at my published image service.
I managed to find an existing tile scheme which had both the projection I wanted and used a PNG tile format. This sorted it for me and my no data values remained transparent once loaded in ArcOnline.
When publishing from ArcMap you have the ability to select the tile format you want but I couldn't seem to find this same setting when publishing a tile service from ArcPro. If you have access to ArcMap, you could try and publish from here instead? - even just to see if that works.
Not sure if the solution will also work for you or if your problem is different but hopefully this may help someone.