Rmv,
Have you considered contacting the US regionals and asking what possibilities there are for a person in your situation ? Air Wisconsin has gotten H1Bs for people in the past albeit very few. Not sure what they're doing these days but asking the question is easy.
There's an Air Wisconsin thread on this website. Someone might know something:
https://www.airlinepilotforums.com/air-wisconsin/
They can't kill ya and eat ya for asking:
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