I commented on this subject a few months ago. I had contacted 2 regionals and a friend of mine has been hired by a regional. One of the regionals is still asking for a degree. Initially one wanted a degree and later sid it wasnt required. The third still isn't taking E3 vis applications.
What I can say is the degree requirement seems to be an airline decision rather than a visa requirement.
I have been contacted by a number of people already working at US regionals. All have said even though the visa requirements seem rigid, the work experience and degree requirement seem to be looked over as long as you he the hours required for an FAA ATP.