I'd be tempted to call someone like Mainfreight if it is just one item.

Is it wrapped/ready for transport?

A furniture moving company may have room in a backload, but I think it would be cheaper/quicker to get a freight company to do it.

Crossing the straight will be expensive.

Unfortunately it's a TM buy, so it's going to need packing at the sending end. 

Packsend could be an option. 

Check with Conroy Removals

They deliver nationwide for Bigsave Furniture so can most likely add an extra piece in on the cheap. (and pack it)

Tried Pack'n'Send. They are getting back to me. Conroy seem ok. More expensive than the The Moving Company if I elect to take out their optional insurance though. Last time I didn't do that - in a full house move - a couple of the boxes didn't turn up, and they (Allied Pickfords) said I had no recourse because I hadn't insured.

I used one of the backload websites ( I forget which one) to find someone last time I needed to do something similar.

Try one of these, cos I can't remember which one I used.

https://www.backload4u.co.nz/

https://www.emptytrucks.co.nz/

http://www.backloadmoving.co.nz/

pbolger:

 

Tried Pack'n'Send. They are getting back to me. Conroy seem ok. More expensive than the The Moving Company if I elect to take out their optional insurance though. Last time I didn't do that - in a full house move - a couple of the boxes didn't turn up, and they (Allied Pickfords) said I had no recourse because I hadn't insured.

 

I hate it when that happens. Same experience with Crown - basically there was nothing they could do (a box went missing).