Alright. It's all about reading the manuals and noticing little things. Those fuse bits are what's actually recommended by the build manual. But that's not what made me change it. The crucial setting is what the fue calculator describes as "Ext. Clock/RC Osc./Low-freq. Crystal: enable internal Capacitors (36 pF) Internal R/C Osc.: leave unchecked! External Crystal: enable full swing (neccessary for >8 MHz)" The important part is "enable full swing" which makes the oscillator circuit go between 0 V and 5 V instead of running on a lower voltage, presumably to save power. This reminded me of something from the FT232BM datasheet.
Input to 6MHz Crystal Oscillator Cell. This pin can also be driven by an external
6MHz clock if required. Note: Switching threshold of this pin is VCC/2, so if driving
from an external source, the source must be driving at 5V CMOS level or AC-
coupled to centre on VCC/2.
So without that fuse bit set, the clock line will not reach the switching threshold and the FTDI chip will not be properly clocked, and USB will not work.
So, now I want to know, is one of the Atmega chips actually broken?
Glad you successfully sorted that out thanks to nitro2k01. There's nothing like building your own stuff.