You should be able to subpoena those e-mails and other documents. Depending on your municipality, there is usually a court/tribunal process just for unemployment claims, or you could get an employment lawyer. It is going to eat up some of that unemployment, but it's worth it to not let a company get away with that kind of shit.
Is it, though? I chose to focus on finding the next gig and luckily got one in a couple weeks. The emotional toll of subjecting yourself to the legal system against an entity with a team of lawyers sounds absolutely horrible.
It's worth it. If there is an actual violation, the company didn't just steal money from you. They defrauded the state labor board and the taxpayers of the state. And that's the sort of thing that government lawyers are very interested pursuing.