Yes I've heard that Eaglejet is recruiting Australians with 1,000 TT but I don't know if anyone has actually been hired this way, or what kind of visa arrangements they might have. It's possible that Eaglejet is simply passing qualified resumes/CVs to Ameriflight or others.
Review of online immigration databases for E3 visas yield no results for Eaglejet nor Ameriflight, though it's possible that these public databases may not be 100% up to date.
May be they can't find Australians with 4 years degree. Honestly, how many pilots in AUS have 4 years bachelor degrees? Since majors in Australia don't require it, most of kids I have seen don't bother with studying in uni.
Let's just hope Trump doesn't mess around with E-3.