Well, I'm glad I checked... It turns out the new watchdog chip was permanently wired disabled.

Fortunately, it has an internal pull-down, so you can leave the enable pin floating and it will be forced-enabled. With that, I verified that it wasn't actually working properly.

One issue is that the default Lfuse value of 0xe0 delays startup for 65 ms, which is way too long. That's been changed to 0xc0, which essentially has no delay. But if startup gets wedged, that's ok, because the watchdog circuit is there to force it to try again. :)

The other issue is that the watchdog seems to impede programming. On AVRs, programming mode is entered by bringing !RESET low, but apparently the start of actual programming has some timing constraints, as it would seem that the watchdog occasionally yanking on the !RESET line during programming is no good. So I'm going to have to spin new boards with a solder jumper to disable the watchdog. You close the jumper for programming and then open it again once programming is complete. It's not ideal, but it will do. The alternative is to not install the chip until programming is complete, but that complicates field firmware updates.