Ok, good suggestion. The results (see below) are more successful, but still confusing:
1. I once again turned off the WiFi on my regular router and turned on the WiFi on the Actiontec, giving it a new never-before-used SSID.
2. I plugged in the Chromecast, expecting it to tell me that it could not connect, and needed setup. Wrong! It connected successfully to the internet. And when I connected my iPod Touch and ran the Chromecast app, it could connect to the Chromecast. My guess is that somehow the Chromecast is remembering WiFi networks by something other than their SSID, and because it had connected to the Actiontec WiFi network before, it was able to reconnect to it even though it had a different SSID! I wouldn't have guessed that.
3. I reset the Chromecast with a long button push, and did the setup from scratch using the iPod Chromecast app. It appeared to go through the setup fine, specifying the new WiFi network and new device name, but when it tried to complete the setup on the Chromecast, something went wrong and the Chromecast got stuck. I eventually pulled the plug and rebooted it. On startup it had the new WiFi network SSID and connected successfully, but the device name had not been changed. The Chromecast app was able to connect to it. The Youtube app was able to see it, but could not play on it.
4. I updated my Chromecast app to the latest version (just in case), did a long-button-push reset again, and went through the entire setup again. This time it completed successfully. The Chromecast app could see the device, and Youtube could see it. But Youtube videos still wouldn't play correctly. The TV screen would blank and show a spinning circle, and the progress bar in the iPod Youtube app would show the video apparently playing, but nothing on the TV screen. I disconnected, updated the Youtube app to the latest version (just in case), tried again several times, different videos - same thing.
5. I got out the Android tablet and gave it a quick test. Same thing: it can see the Chromecast, but can't play anything on it.
6. I tried the set-security-to-High trick on the Actiontec. No help. Put it back to NAT-only.
6. I unplugged and rebooted the Chromecast again. It reconnected fine, and now everything suddenly worked. Youtube and a couple of other apps were able to play media successfully on the Chromecast from both the iPod and the Android tablet.
7. Everything was fine until I tried Netflix. The Chromecast went into the Netflix app successfully and loaded the content to 100%. Then it went back to 0% and tried again. Then it exited without playing anything, and the Netflix app on the iPod crashed and exited. I unplugged and rebooted the Chromecast again, tried Netflix again with the same video, and this time everything was fine. Another unplug and reboot, and everything stayed fine - for the moment.
8. I switched the WiFi back, did a long reset on the Chromecast and reconnected it to my normal router, did the setup again, gave it a quick test.. That all went perfectly smoothly, unlike the Actiontec.
So what can we conclude from this? The Chromecast definitely can work on the Telus Actiontec V1000H, but it's erratic. I encountered problems several times, and although each time I was able to get past the problem, I don't understand how or why. It might stabilize in long-term use, or it could be a frequent annoyance.
BTW, one other observation: I specified the country as United States during setup (as usual), and indeed the country code shown in the Chromecast properties after setup was United States as specified and remained so through several power cycles - even though I'm using Telus, a Canadian ISP.