For some reason (likely operator error), I couldn't get a link to the PDF for this bit but...there was an airline labor and employment symposium earlier this year (never heard of FordHarrison) where the subject of the US airlines hiring expats was one of the topics. Use of E3s was apparently on the docket there. Google this and it'll lead you to the symposium schedule:
FordHarrison airline labor and employment symposium
10:00 AM - 10:45 AM
RECRUITING FOREIGN PILOTS TO SOLVE STAFFING SHORTAGES
With pilot shortages at critical levels throughout the industry, many airlines are looking to recruit from outside the U.S. borders. What do you need to know about the use of E-3 visas?
Geetha Adinata, Partner, FordHarrison LLP