How would I have done it?
The easiest way would have been to tell Ben I want to meet with you in the morning, give him what he'd already know was about to happen—his termination, and then send out an invitation for the local press to a press conference at 10 AM, where the firing would be announced and questions answered (even though not much would be said).
But if it couldn't wait, after the conversation last night, send out a notice for a press conference at 8 AM to the local press, alerting Ben it was going out and letting him see it first so he had full visibility into what was happening. By all accounts that would have been before midnight.
It still would have been late, but there would have been enough time for the press to be on campus at 8AM for the formal announcement. Yes, everyone would have known EXACTLY what this morning's press conference was about. No, it wouldn't have been an obvious attempt to sidestep standing in front of the press and handling questions, which an AD should have done in this case.