Im in Perth and I fly in an out of oz with the bikes a couple of times a year. I now just have a set of tyres in the UK which I take off and leave there and another set I leave in OZ rather than try and clean them sufficiently.
I have come in with tyres before but always makes sure I have fresh rubber on. I think I've only had my bag opened once or twice. As long as its decently clean I've never had any bother.
I usually put my slightly uncleanable 5:10's in a sealed plastic bag somewhere else in my luggage.
Going in to NZ is a whole different kettle of fish - flown in to Queenstown a couple of times and they are pretty militant on how clean everything has to be.
From a flying point of view - Qatar are pretty damn good when it comes to flying with bikes - get a free 10kg of sports equipment on top of normal luggage allowance and the per kg charges over and above are pretty reasonable. If you are on the frequent flyer program - two returns london - perth gets you to Bronze membership and another 10kg of additional luggage. Plus the service is excellent.