Just got off the phone with my ISP's tech support and while she couldn't say for certain, she said it appears that IRC has been declared "dangerous" and that connections are being blocked. And there's really nothing to be done about it.
Moving to a different ISP isn't an option, because there are no other ISPs around here - I live in a very rural region. I can run a VPN, which I have no interest in doing, or... I can do without. Unless someone has another idea? I'm open to just about anything at this point.