AT&T called today to follow up on my less-than-satisfied exit survey. They're going to send someone to replace the modem/router/gateway device. I don't think this will help.
The good: they acknowledged the problem persists, they explicitly acknowledged that I'm correct that the available information suggests it's not a configuration issue or an issue with my personal equipment.
The bad: I sincerely doubt replacing this device will work either, though I guess we'll see. [My bet is still on a configuration issue with one/some of the devices internal to AT&T's network. I also still suspect this is the same as the intermittent DW->AT&T email problem.]
Connection is good today, and was good yesterday, but I expect it'll go away again in the next few days.
Also, while my appointment for the modem repair is sometime this evening in the 4-9 range, I've seen an AT&T van driving around through the parking lot for the last hour or so. They just went by again for the third time. They seem to be looking for something.