Airport Extreme Guest network has (almost) no Internet connection

First off: My modem is in bridge mode according to some instructions I found, and the Time Capsule is in "DHCP and NAT" mode. 

Still, my Guest network has almost no Internet connection. I say almost because some sites do connect: https://openwireless.org and https://1.1.1.1 (and https://one.one.one.one) are two that I've found. Nothing else seems to load, however, and pings time out. This doesn't seem to be a DNS issue, because DNS lookup in Network Utility works fine, even for sites that won't load. The Speedtest app will find a server to connect to, and then report "Could not connect to the Internet." Safari reports "Safari can't connect to the server" on nearly all sites, including Apple and Dropbox.

The main network works fine; only the Guest network is affected. This worked fine at one point with this same modem/router setup, but I've since updated the Time Capsule to 7.9.1. That may or may not be what caused the issue; I don't test my Guest network on a regular basis.

Any clues as to what could be going on here? I've been liking not having to give guests my WiFi password.