Under a "reasonable expectation of privacy" analysis, you would probably not run into any problems with respect to the state's wiretapping laws. Professors are speaking to large groups of people, and they probably do so with doors open from time to time, or loudly enough to be heard through the doors, undercutting any expectation of privacy.
But I suspect you might run into problems in terms of trespassing. I don't know Florida's laws, but they are frequently written to cover people who remain in a place while doing something that they know is against the rules for being in that place. More frequently, this applies to someone who comes gets into a fight inside someone else's house -- they might have been invited in, but once they started beating the homeowner, they should have known that they were no longer welcome. Your case is not as egregious, but the egregiousness is not the point. You're not allowed to be recording lectures in the classroom, so you're not allowed in the classroom if you're recording.
Of course, beyond the questions of criminal law, there's also the question of complying with school policies, which I would expect to be the more likely avenue for disciplinary action.
Beyond all that is the question of whether the First Amendment permits either kind of criminal penalty, so the fact that this is a public institution does make a difference. There's a decent argument that enforcing either of these laws to your situation would violate your First Amendment rights to receive or disseminate information -- analogize it to recording a police interaction -- but I supsect you'd have a difficult time turning that argument into anything helpful without the assistance of a lawyer.