Reset device, connect wirelessly, then access http://tplinkap.net; this brings up the device's web UI.
The two choices seem to be "Bridge with AP mode" or "Client mode"; I'm not actually sure how they each function differently. "Bridge with AP mode" doesn't seem to work, so trying "Client mode" with DHCP off (let the phone do DHCP).
Some information from the device:
- device ("LAN") IP: 192.168.0.29.
- main router MAC: CC-61-E5-BE-CF-BE
- ...where in this case the "main router" is the phone
Then press [finish] button, which reboots the device. After that, device's SSID no longer shows up. Connecting to the main network (router is already configured to talk to the device), the UI is accessible through http://192.168.0.29... and we have internet.
(Caveat: actually, we didn't; I was still getting a trickle through another connection. This was the right mode, however.)