So I came over a few years ago and got my FAA commercial certificate (yes, it's a certificate here). Initially the private on the basis of my CASA license and then got my commercial and instrument. I'm not an instructor and didn't go that way. I came over with 1500 hours TT, incl. about 750 AS350 series.
Both jobs I've had here, the companies would not have bothered running around jumping through hoops for the E3 visa. Firstly because they wouldn't want to deal with more hassle and second because there's waaay too many out of work pilots for them to even want to do more work to find someone, when they could look to the ever-growing pile of resumes sitting on the Chief's desk.
If you've read Bladeslapper you've probably seen 1-2 members advocating that pilots come over on an E3. That may work for medium/heavy jobs, where a particular type rating or skill set is needed, but for a light single, no way. Where the E3 seems to be working well is in the airlines where recruiting firms are used. The only recruiting done for rotary, to my knowledge, is in EMS with Aviation Search Group. You may want to give them a call and ask specifically if with your hours/experience, if you came over and got your commercial and IR, would they then proceed with the paperwork. You could also just try the companies direct and see what they say, my reply is only my opinion of how it is here.
I wish you luck. The industry here is far better than in Oz, with far more opportunities. Maybe just come for a vacation, find your future partner and go that way... ;-)