Thanks for taking a look. Both my board and the one in the image (not mine, pulled from Flickr) have the solder bridge between Vcc and *RESET, so it's probably deliberate.
Absence of a decoupling capacitor probably wouldn't explain the specific problems I'm seeing*, so it's possible the FTDI chip itself has been damaged.
- USB->serial to the AVR works fine; serial->USB from the AVR is OK up to and including the FTDI input pin, but after that I don't see any activity. (Other FTDI devices function properly, so I don't suspect host configuration issues.)