The AirPort Utility tries too hard to be friendly. It wants to do some fancy migration from an older device that’s running, but I’d already exported that configuration file and removed it. Everything was connected, I just wanted to import the configuration file.
The trick, of course, is the option key. Cancel out and look for “Other Wi-Fi Devices”. Option-click the new one. You get a ‘power user’ interface (same one with option clicking any device in AirPort Utility). Now you can import the .baseconfig file you exported previously.
It came up perfectly, except it had some odd default password initially. I changed it to my admin password and updated.