I recently came across Blue River Dairy at the Food Show here in Auckland who make a couple of organic cows milk cheeses.
I'm dairy intolerant, so I just LOVE their range of sheeps milk cheeses (all vegetarian), including a fantastic cheddar.
Milton Vineyard in Gisborne is excellent and biodynamic
Very good Chenin Blanc, one of very few in the country, also excellent Riesling too, Opou I think!
While there try TW wines who do a very good sweet wine, depending on year the grape can change, I had a viognier and it was fantastic.
Enjoy your trip
Don't know what "later this year means but if you're here in Aug check this out. You'll find some links there too.
Also check out www.hohepa.com. Its a pretty special place.
http://www.nzsca.org.nz has a cheese map, but you'll have to fish out the organic stuff.
www.seresin.co.nz is organic/biodynamic- also does oil and honey but don't know about cheese.
I suppose you know about wwoofers? (willing workers on organic farms?) If not check out www.wwoof.co.nz (or just .org if you want the international sites.)
Keep us posted on what you get up to,
I don't claim any expertise but I did stop at this cheese maker (in Northland) and it appears that they qualify. You can visit the farm which has a store on site, but apparently they don't allow tours.
There is Whitestone which is in Oamaru, don't know if they meet the criteria but they have a tour
Maybe Canterbury Cheesemongers could give you some recommendations.