I just discovered why Webgizmo didn't seem to work over WAN - I'm on my workplace WiFi all day, and I can't connect to my MC that way. I accidentally turned WiFi off just now, and it works fine over 3G. It also works fine via my WLAN at home. So my router is configured properly and MC is working fine. But if I'm accessing the internet via external WLAN, I can't get into it.
This is almost certainly not a MC issue, nor is it likely to have anything to do with Linux. But I have no idea what the problem might be. I can access the Serve-to-Me and Tonido servers on my home network using WiFi at work to reach the internet, and I play Spotify throughout the day. So I doubt very much that it's a firewall issue at work. I'm going to activate my home VPN and see if that enables web access from a remote WLAN. If I learn anything useful, I'll post it here.
Thanks again for all the help, everyone. I'll add what I can to keep the ball rolling.