There is an "O" visa for persons of extraordinary ability. You need to have a job offer.
Here is a link that gives you more detail about the visa requirements. The employer would have to file the petition on your behalf.
It seems you may be a candidate for such a visa given the fact you have an international reputation both down under and abroad in the EU.
I would strongly suggest that you pursue that salon who showed interest in you and offer to pay the legal fees for this visa.
That way they have nothing to loose and everything to gain. If you read that link and really believe you qualify go to this link to find a lawyer in NYC that does employment based work and check their websites to see if they are skilled in O visas.
This firm has good reputation http://cyrusmehta.com/
We are used to working remotely with clients who are in countries outside the US to get them visas so distance is not an issue.
You do not qualify for the E3 because that requires a Bachelor Degree and the job duties require the degree as well. Stylist is not in that category.
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