I moved back to Oz from the ME last year with an SS, and SL and an ST4. One was originally purchased in Oz, one was bought in Singapore (but has Oz compliance plates), the third had never heard of Oz!
In that process I learnt everything about this stuff.
It's not the US Dept of Transport that you need to care about, but Oz goverment. It does NOT have to comply with Australian ADRs (one-offs can be imported) and compliance has little to do with how strict it is in Europe or whatever. Compliance has to do whether Ducati (not Frasers) will state that this is Oz compliant or not. I tried to bring in a 749 at the same time as the above: Frasers were helpful, but couldn't issue any letter re. compliance unless Ducati sPa said so. Ducati said, no, sorry, this is Euro Spec, not Oz, so we can't pledge compliance.
Rules of compliance have silly things like whether the windshield shatters or cracks. remember how the first 916s in Oz all had single lens headlights (not the twin lights?) This was a compliance issue.
My SL is not ADR compliant, but can be registered: I get a "Personal Import" compliance plate.
To be honest, unless you really really really think no other ST3 is going to match your own, it's a lot easier to sell it in the US and buy another one here.
Costs: There is a cost of shipping which isn't unsubstantial, but is okay. You have to have it steam-cleaned (and provide evidence of same). If Oz customs don't think it has been, they'll do it for you. At their own $ p/h figure. Then there's the magical formula by which GST is calculated: either on your say so (of the purchase price) or on custom's say so. There's also a pest inspection fee, and possibly fumigation if they think there's a grain of dirt on it. This could also include the removal of the tires if they have tiny cracks in the sidewalls...
I have heard of people who shipped and THEN applied, only to have to face storage costs in Oz customs.
But best of all... you HAVE to be able to prove: a) that you have owned it for the past 12 months; b) show that it was registered in your name in that time; and c) prove (passport) that you and the bike pretty well lived in the same country during that time.
If it's an '05 and is less than 12 months old, don't even bother trying!
PM me and we can email back and forth on it.