Airport Extreme can't be set to extend existing network

My vacation home's WiFi network is provided by my ISP's (Time Warner) router. I have an Airport Extreme that used to be configured to provide the WiFi network on another property, and I'd like to use it to extend the existing network on the TWC router.

I had a lot of difficulty doing a factory reset on the Airport Extreme, but I'm pretty sure I've succeeded (by powering up with the reset button depressed) after several attempts. At least the Extreme doesn't show any signs of the old network it provided.

When I try to configure it in Airport Utility, it only wants to create a new network. If I click on "Other Options" and select "Add to an Existing Network", the next screen is titled "This Airport Extreme will create a network", and prompts for a new network name and password. (Specifying the current network name generates an error because the network already exists, as I'd expect for creating a new network.)

Any ideas on how to finesse this Airport Extreme into extending a network?

TIA,

Doug

P.S. I have considered plugging the Extreme into one of the TWC router's EtherNet ports and creating it's own WiFi network (with the benefit of adding 5GHz support), but the last time I tried that I lost all connectivity; I'm concerned that the ISP network might be protecting against over-extending the network, although the glitch may have been coincidental. If anyone has experience/ideas about this alternate configuration, I might be willing to try again.