That was a surprisingly good try by the AT&T support tech. Three or more years ago I myself might have suggested you try that but IPv6 implementations have completely settled down now. I personally haven't seen a networking problem I could diagnose to an IPv6 implementation problem in about 6 years (they were common 10+ years ago).
I did have one other idea for a possible fix just now. Try a complete power cycle of your entire network. By this I mean literally completely power down of every single network device, some may require pulling an ac power cord to truly power down. This includes iPods, iPads, PCs, routers, modems, switches, hubs, Game consoles, streaming TV devices, etc.
Wait a couple minutes then start powering up the devices one at a time. Power up in rough order of closeness to the physical incoming wire and let each device fully initialize before moving on to the next device. e.g. Modem, wired router, switches/hubs, wired devices, wireless access point, wireless devices. Don't worry if you don't know exactly which devices of yours correspond to the names I've written, basically follow the wires and do all wires first then wireless. This will probably take a quite a few minutes to accomplish so make sure your household is ready to be without the internet for an hour when you start.
If that doesn't fix things, and the problem doesn't self correct, then I recommend you find someone local who knows how to use advanced network diagnostic tools (e.g. Wire Shark). I'm certain that if I could be physically at your house with all my bag of tools I could nail down the actual cause of this odd problem.