Do you want the www or not?
If you remove it now, you run the risk of people who visit the site frequently being stuck in a redirect loop and not being able to visit your site. When a browser receives a 301 redirect it caches it, very stubbornly. If you now change the 301 to point back to the original location your frequent visitors browsers will have cached the 301 that points from non-www to www, and if www returns a 301 that points to non-www, they'll just be stuck in a loop. If you want to go back I would try to make turn the current 301 from non-www to www into a 302, then change back in several days or weeks. That might not be very great for your SEO, though.
If you want to stick with the www, then stick with it. I'm not sure what I was seeing earlier, but when I check your homepage now with curl the non-www redirects me to www, as expected:
Johns-MBP:~ John$ curl -I http://mefco.co.nz
HTTP/1.1 301 Moved Permanently
Date: Sat, 19 Mar 2016 20:38:22 GMT
Server: Apache/2.2.31 (Unix) mod_ssl/2.2.31 OpenSSL/1.0.1e-fips mod_bwlimited/1.4
X-Powered-By: PHP/5.6.16
X-Pingback: http://www.mefco.co.nz/xmlrpc.php
Location: http://www.mefco.co.nz/
Cache-Control: max-age=604800
Expires: Sat, 26 Mar 2016 20:38:22 GMT
Vary: User-Agent,Accept-Encoding
Content-Type: text/html; charset=UTF-8
Johns-MBP:~ John$
Where did you get the canonical info you posted above, is it from Moz? If so, it's probably outdated information. Remember what Matt wrote above about Moz & Google taking time to re-crawl your site. The way to check what your canonical tag, if any, says right now is to view the page source, ( in Chrome: View > Developer > View Source), and look for it, (Ctrl/Cmd + F to Find in the source, then type "canonical"). In your case, your canonical is now set to the www- URL - I'm not sure if you changed it since Matt looked, or if a cache expired, but it appears correct now.
You could go through any HTTP 301 and canonical settings in the Yoast SEO plugin, (which I see you're using), but I don't think you're at that point yet. Go through and make sure everything's set to www, if that's what you want to use. Really, I think you're almost there, and probably at a point where you should wait a few days to see what happens. I made a huge change on our site last weekend, (changed 99% of our URL structure), and after a bit of bug-fixing during the week we're only seeing the start of the result in Google & Moz now.