I'm a recruiting manager in Sydney (also a UK expat working in IT), I've been here for 10 years and I work for the NSW government (yes, it's a strange one, I'm still on a 457!).
Looking at your LinkedIn profile DavLap, you look like a great guy. I would say however that your problem is that helpdesk/application support is more the domain of people with less experience than you. It's also now often out-sourced to the vendor/managed services, which are more and more likely to be off-shore these days. I would look at a person with your experience/age as being a service desk manager or specialist assisting with helpesk transition or dealing with managed services. These roles don't come up too often though, so I can understand your difficulty.
You say you've worked as a solution architect before - have you tried re-jigging your CV to get an architect role? There are plenty of SA roles going, in your technology area and age is an asset. Or actually, your skills seem very suited to integration architecture and service bus work, that seems big business at the moment - we've just delivered a service bus and are working on our integration patterns. While it all seems "service bus mumbo jumbo" in reality it's all quite practical integration patterns such as SQL and FTP alongside the web services, particularly into ERPs.
Updating your skills to include Tibco and other service bus applications would give your CV a really good boost. In your shoes I would probably say "but I won't have hands-on" but I don't see why you can't build yourself a little Tibco lab at home and get some real hands-on - I've just used an AWS certified cloud engineer who had the certification but not much hands-on aside from the course (which was lab based) - no problems at all. What have you got to lose?
When I recruit I either approach candidates directly, using LinkedIn (the AU market is small and I can usually find a contact who has previously worked with that person for a reference before I approach them) or use a couple of my preferred agencies. These agencies are the ones I've had a good experience with as a candidate in the past and who I trust - their good treatment of me as a candidate is now rewarded by me giving them business. Others I won't touch because of their attitude/poor ethics. This applies mainly to contract roles - for perm we have to follow a very specific process.
I personally don't care about Australian experience - I find most overseas candidates from the UK have a better work ethic. I do know that it happens here though, ditto for people trying to move to Brisbane from Sydney.