but seemingly based on that originating IP, the connection is either working correctly, or immediately closed again by the host.

Oh, so it's not DNS, I'll bet it's some kind of a routing problem.

I've had that sort of thing happen before. In fact, it was with this BBS. My home connection could see it and my work connection could not see it. A traceroute revealed that the transatlantic link was the fault. One of them was down, and depending on which ISP I was dialed into, the packets were routed two different ways.