Blair,
I play flanker here in the States for a college team, and have grappled competitively with a lot of success. The major difference in lifting pans that has helped me has been the issue of muscle mass. It's great for me in rugby to be about 210pounds or just under 100 kilos at 5'11"-6'0" tall. I'm about exactly 182 centimeters.
In fighting you're going to have weight classes and you might worry about keeping mass that's more appropriate to your frame. In any case, rarely will another fighter be trying to run away or through you, so that big momentum bonus from running with WEIGHT isn't there. You want to be as strong and as light as possible. 5x5 is great for development, but afterwards you might want to switch to a lower rep scheme and train for outright explosive strength. When I grapple while not playing rugby, the strength I lose when going from 210pounds to 189 is almost negligible, but there's a big difference between fighting in the 190 and under class and fighting in the 205+ class. BIG difference.
Bodybuilding isn't evil, and can be wildly beneficial, especially when you want some injury-preventing, shock-absorbing, hit-delivering, mean momentum muscle. What you want for MMA (IN MY OPINION AND OWN EXPERIENCE) is explosive strength. I personally feel the anaerobic, all-out with a short rest style conditioning of rugby translates very well to grappling and MMA.
Also, I'll be traveling to New Zealand in November and staying for three to six months while working socially with collective organic farms. In America (especially where I live) the local club teams are set up in a way that you can walk up to a practice and talk with them, get to know the guys, and train with them for a while. Maybe they won't start you, maybe they won't play you at all, maybe they would like dues before you start practicing, but they'll almost always let you train with them. Is it like this in New Zealand? Or, how best could I go about training as much rugby as possible while I'm there? I'm 22, if it matters.
Good luck!
Nick