The FE-5680A board can support the 5680A, the variant of the 5660A with firmware modified by Skip Withrow, and the FE-405B. It just requires different firmware for the FE-405B (and for the 5680A, it requires some adjustment to the solder jumpers).

Replacing the firmware is a bit tricky, though, since sending garbage to an FEI oscillator over its serial port can brick it if you're not lucky. But you can't program the ATMel controller without a clock source, so you can't disconnect the oscillator, load the new firmware, and then connect the new oscillator.

The solution is to erase the firmware while it's connected to the old oscillator (avrdude -c [programmer] -p m328pb -U flash:w:0:m), then move the board to the new oscillator and load the new firmware.

While the flash is erased, the controller won't even configure, much less transmit on the serial ports, so there's no chance it will send garbage. In actual fact, there's little chance it would anyway, since when you switch from the 56x0A to the 405B you change from 10 MHz to 15 MHz, and the serial port clock generator will have the wrong constants, meaning it won't be able to properly parse the data from the GPS receiver. Without detecting a GPS lock, it shouldn't want to talk to the oscillator at all. But to be extra sure, I recommend following this procedure if you want to switch between the 56x0A and 405B.